world_chair_reference = 'As ground truth reference, "forward" motion in the world corresponds to motion toward the workspace camera view, "upward" motion in the world corresponds to motion up from the workspace camera view image, and "right" motion in the world corresponds to motion to the left of the workspace camera view image.'
world_table_reference = 'As ground truth reference for world motion relative to the robot, "forward" motion in the world corresponds to motion down the workspace camera view image, "upward" and "downward" motion in the world corresponds to motion out of and into, respectively, the the workspace camera view image, and "right" motion in the world corresponds to motion to the left of the workspace camera view image. '

wkspc_w_thinker = """
Given the user instruction and an image of the robot workspace, generate a structured physical plan for a robot end-effector interacting with the environment.
The task is to {task} while grasping the {obj}.

The robot is controlled using position and torque-based control, with access to contact feedback and 6D motion capabilities. 
Motions can include grasping, lifting, pushing, tapping, sliding, rotating, or any interaction with objects or surfaces.
Motion can resolve across multiple axes, so be careful to consider all axes of motion to accomplish the task.

Reason about the provided and implicit information in the images and task description to generate a structured plan for the robot's motion. Think about:
- Object geometry and contact points (from the image)
- Force/torque sensing at the wrist
- Prior knowledge of object material types and mass estimates
- Environmental knowledge (table, gravity, hinge resistance, etc.)

The robot workspace view labeled with the axes of motion relative to the wrist of the robot, placed at the point of grasping. The wrist of the robot may be oriented differently from the canonical world-axes, so this workspace view may help understand the wrist-relative motion to accomplish the task in the world.
World Motion Reference: {world_reference}
Use physical reasoning to complete the following plan in a structured format. Carefully map the required motion in the world to the required motion, forces, and torques at the wrist.

[start of motion plan]
The task is to {task} while grasping the {obj}.

Mapping World Motion to Wrist Motion:
The provided workspace image confirms {{DESCRIPTION: the object and environment in the image and their properties, such as spatial relationships, color, shape, and material, and their correspondence to the requested task}}.
The labeled wrist axes correspond to the world as such: {{DESCRIPTION: describe in detail the labeled wrist frame's axes of motion and their correspondence to the motion in the depicted world, utilizing the provided World Motion Reference}}.
The blue axis represents wrist Z-axis motion. It roughly corresponds to {{DESCRIPTION: describe the wrist Z-axis (positive and negative) motion to motion in the world with careful analysis.}}.
Based off knowledge of the task and motion, in the wrist Z-axis, the object must move {{DESCRIPTION: the object's required motion in the wrist Z-axis to accomplish the task}}.
The red axis represents wrist X-axis motion. It roughly corresponds to {{DESCRIPTION: describe the wrist X-axis (positive and negative) motion to motion in the world with careful analysis.}}.
Based off knowledge of the task and motion, in the wrist X-axis, the object must move {{DESCRIPTION: the object's required motion in the wrist X-axis to accomplish the task}}.
The green axis represents wrist Y-axis motion. It roughly corresponds to {{DESCRIPTION: describe the wrist Y-axis (positive and negative) motion to motion in the world with careful analysis.}}.
Based off knowledge of the task and motion, in the wrist Y-axis, the object must move {{DESCRIPTION: the object's required motion in the wrist Y-axis to accomplish the task}}.
To accomplish the task in the wrist frame, the object must be moved {{DESCRIPTION: the object's required motion in the wrist frame to accomplish the task}}.

Understanding Robot-Applied Forces and Torques to Move Object in the Wrist Frame:
To estimate the forces and torques required to accomplish {task} while grasping the {obj}, we must consider the following:
- Object Properties: {{DESCRIPTION: Think very carefully about the estimated mass, material, stiffness, friction coefficient of the object based off the visual information and semantic knowledge about the object. If object is articulated, do the same reasoning for whatever joint / degree of freedom enables motion. }}.
- Environmental Factors: {{DESCRIPTION: Think very carefully about the various environmental factors in task like gravity, surface friction, damping, hinge resistance that would interact with the object over the course of the task}}.
- The relevant object is {{DESCRIPTION: describe the object and its properties}} has mass {{NUM}} kg and, with the robot gripper, has a static friction coefficient of {{NUM}}.
- The surface of interaction is {{DESCRIPTION: describe the surface and its properties}} has a static friction coefficient of {{NUM}} with the object.
- Contact Types: {{DESCRIPTION: consideration of various contacts such as edge contact, maintaining surface contact, maintaining a pinch grasp, etc.}}.
- Motion Type: {{DESCRIPTION: consideration of forceful motion(s) involved in accomplishing task such as pushing forward while pressing down, rotating around hinge by pulling up and out, or sliding while maintaining contact}}.
- Contact Considerations: {{DESCRIPTION: explicitly consider whether additional axes of force are required to maintain contact with the object, robot, and environment and accomplish the motion goal}}.
- Motion along axes: {{DESCRIPTION: e.g., the robot exerts motion in a “linear,” “rotational,” “some combination” fashion along the wrist's [x, y, z, rx, ry, rz] axes}}.
- Task duration: {{DESCRIPTION: reasoning about the task motion, forces, and other properties to determine an approximate time duration of the task, which must be positive}}.

Physical Model (if applicable):
- Relevant quantities and estimates: {{DESCRIPTION: include any relevant quantities and estimates used in the calculations}}.
- Relevant equations: {{DESCRIPTION: include any relevant equations used in the calculations}}.
- Relevant assumptions: {{DESCRIPTION: include any relevant assumptions made in the calculations}}.
- Computations: {{DESCRIPTION: include in full detail any relevant calculations using the above information}}.
- Force/torque motion computations with object of mass {{NUM}} kg and static friction coefficient of {{NUM}} along the surface: {{DESCRIPTION: for the derived or estimated motion, compute the force required to overcome friction and achieve the task}}.

Wrist Force/Torque Motion Estimation:
Linear X-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [positive, negative, no]}} force along the X-axis with magnitude {{PNUM}} N.
Linear Y-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [positive, negative, no]}} force along the Y-axis with magnitude {{PNUM}} N.
Linear Z-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: linear [positive, negative, no]}} force along the Z-axis with magnitude {{PNUM}} N.
Angular X-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the X-axis with magnitude {{PNUM}} N-m.
Angular Y-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Y-axis with magnitude {{PNUM}} N-m.
Angular Z-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Z-axis with magnitude {{PNUM}} N-m.
Grasping force:  {{DESCRIPTION: estimated force range and justification based on friction, mass, resistance}}, thus {{PNUM}} to {{PNUM}} N .

Python Code with Final Motion Plan:
```python
# succinct text description of the explicit estimated physical properties of the object, including mass, material, friction coefficients, etc.
property_description = "{{DESCRIPTION: describe succinctly the object and its properties}}"
# succinct text description of the motion plan along the wrist axes
wrist_motion_description = "{{DESCRIPTION: the object's required position motion in the wrist frame to accomplish the task}}"
# the vector (sign of direction * magnitude) of motion across the wrist axes [x, y ,z]. 
wrist_motion_vector = [{{NUM}}, {{NUM}}, {{NUM}}]
# the vector (sign of direction * magnitude) of the forces and torques along the wrist's [x, y, z, rx, ry, rz] axes
wrist_wrench = [{{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}]
# the grasping force, which must be positive
grasp_force = {{PNUM}}
# the task duration, which must be positive
duration = {{PNUM}}
```
[end of motion plan]

Rules:
1. Replace all {{DESCRIPTION: ...}}, {{PNUM}}, {{NUM}}, and {{CHOICE: ...}} entries with specific values or statements. For example, {{PNUM}} should be replaced with a number like 0.5. This is very important for downstream parsing!!
2. Use best physical reasoning based on known robot/environmental capabilities. Remember that the robot may have to exert forces in additional axes compared to the motion direction axes in order to maintain contacts between the object, robot, and environment.
3. Always include motion for all axes of motion, even if it's "No motion required."
4. Keep the explanation concise but physically grounded. Prioritize interpretability and reproducibility.
5. Use common sense where exact properties are ambiguous, and explain assumptions.
6. Do not include any sections outside the start/end blocks or add non-specified bullet points.
7. Make sure to provide the final python code for each requested force in a code block. Remember to fully replace the placeholder text with the actual values!
8. Do not abbreviate the prompt when generating the response. Fully reproduce the template, but filled in with your reasoning.
9. Make sure to refer to the provided correspondence in the direction guide between motion in the world frame and positive/negative motion in the respective axes.
"""

ww_3w_thinker = """
Given the user instruction and a two images containing a third-person view on the left, and a robot wrist view on the right, generate a structured physical plan for a robot end-effector interacting with the environment.
The task is to {task} while grasping the {obj}.

The robot is controlled using position and torque-based control, with access to contact feedback and 6D motion capabilities. 
Motions can include grasping, lifting, pushing, tapping, sliding, rotating, or any interaction with objects or surfaces.

Reason about the provided and implicit information in the images and task description to generate a structured plan for the robot's motion. Think about:
- Object geometry and contact points (from the image)
- Force/torque sensing at the wrist
- Prior knowledge of object material types and mass estimates
- Environmental knowledge (table, gravity, hinge resistance, etc.)

The robot workspace view labeled with the axes of motion relative to the wrist of the robot, placed at the point of grasping. The wrist of the robot may be oriented differently from the canonical world-axes, so this workspace view may help understand the wrist-relative motion to accomplish the task in the world.
The robot-wrist view labeled with the axes of motion relative to the wrist of the robot. This close up view of the wrist may help understand more precise wrist-relative motion, especially since the wrist will be attached, via the robot end-effector, directly to the object and moving it.
World Motion Reference: {world_reference}
Use physical reasoning to complete the following plan in a structured format. First look at the workspace-view image to carefully map the required motion in the world to the required motion, forces, and torques at the wrist.
However, the labelled wrist coordinate frames will likely differ or even be opposite of this description, so we must carefully analyze the images to understand the mapping of wrist motion to the world.
Do not overfit to the wrist view, as it is not a global perspective. For example, even though the wrist-view red X-axis points up the image, does not necessarily mean that the wrist X-axis corresponds to upward motion. The workspace view is more global and should help determine world motion, primarily, and the wrist view is more local. Use the wrist view to clarify ambiguities in the workspace view if motion is not clear.

[start of motion plan]
The task is to {task} while grasping the {obj}.

Mapping World Motion to Wrist Motion:
The provided images with workspace and wrist views confirm {{DESCRIPTION: the object and environment in the image and their properties, such as color, shape, and material, and their correspondence to the requested task}}.
The red axis in the workspace-view image represents wrist X-axis motion. It roughly corresponds to {{DESCRIPTION: describe the wrist X-axis motion to motion in the world, including negative and positive motion (the labelled axis arrow points in the direction of wrist-axis relative positive motion). It can correspond to arbitrary motion, so analyize the labeled axis carefully.}}.
The green axis in the workspace-view image represents wrist Y-axis motion. It roughly corresponds to {{DESCRIPTION: describe the wrist Y-axis motion to motion in the world, including negative and positive motion (the labelled axis arrow points in the direction of wrist-axis relative positive motion). It can correspond to arbitrary motion, so analyize the labeled axis carefully.}}.
The blue axis in the workspace-view image represents wrist Z-axis motion. It roughly corresponds to {{DESCRIPTION: describe the wrist Z-axis motion to motion in the world, including negative and positive motion (the labelled axis arrow points in the direction of wrist-axis relative positive motion). It can correspond to arbitrary motion, so analyize the labeled axis carefully.}}.

The image with the labeled wrist axes shows the wrist frame of the robot {{DESCRIPTION: describe the wrist frame and its axes of motion}}. Now, with an understanding of wrist-relative motion in the world from the workspace view, we can potentially provide more accurate wrist-relative motion by analyzing the wrist-view image. 
With this close up view of the red wrist X-axis, we can update the wrist X-axis motion to move {{DESCRIPTION: describe any updated wrist X-axis motion determined via analysis of the wrist-view image}}.
With this close up view of the green wrist Y-axis, we can update the wrist Y-axis motion to move {{DESCRIPTION: describe any updated wrist Y-axis motion determined via analysis of the wrist-view image}}.
With this close up view of the blue dot into the page representing wrist Z-axis, we can update the wrist Z-axis motion to move {{DESCRIPTION: describe any updated wrist Z-axis motion determined via analysis of the wrist-view image}}.

Based off knowledge of the task and motion, in the wrist X-axis, the object must have {{CHOICE: [positive, negative, no]}} motion with magnitude {{NUM}} m.
Based off knowledge of the task and motion, in the wrist Y-axis, the object must have {{CHOICE: [positive, negative, no]}} motion with magnitude {{NUM}} m.
Based off knowledge of the task and motion, in the wrist Z-axis, the object must have {{CHOICE: [positive, negative, no]}} motion with magnitude {{NUM}} m.
To accomplish the task in the wrist frame, the object must be moved {{DESCRIPTION: the object's required motion in the wrist frame to accomplish the task}}.

Understanding Robot-Applied Forces and Torques to Move Object in the Wrist Frame:
To estimate the forces and torques required to accomplish {task} while grasping the {obj}, we must consider the following:
- Object Properties: {{DESCRIPTION: Think very carefully about the estimated mass, material, stiffness, friction coefficient of the object based off the visual information and semantic knowledge about the object. If object is articulated, do the same reasoning for whatever joint / degree of freedom enables motion. }}.
- Environmental Factors: {{DESCRIPTION: Think very carefully about the various environmental factors in task like gravity, surface friction, damping, hinge resistance that would interact with the object over the course of the task}}.
- The relevant object is {{DESCRIPTION: describe the object and its properties}} has mass {{NUM}} kg and, with the robot gripper, has a static friction coefficient of {{NUM}}.
- The surface of interaction is {{DESCRIPTION: describe the surface and its properties}} has a static friction coefficient of {{NUM}} with the object.
- Contact Types: {{DESCRIPTION: consideration of various contacts such as edge contact, maintaining surface contact, maintaining a pinch grasp, etc.}}.
- Motion Type: {{DESCRIPTION: consideration of forceful motion(s) involved in accomplishing task such as pushing forward while pressing down, rotating around hinge by pulling up and out, or sliding while maintaining contact}}.
- Contact Considerations: {{DESCRIPTION: explicitly consider whether additional axes of force are required to maintain contact with the object, robot, and environment and accomplish the motion goal}}.
- Motion along axes: {{DESCRIPTION: e.g., the robot exerts motion in a “linear,” “rotational,” “some combination” fashion along the wrist's [x, y, z, rx, ry, rz] axes}}.
- Task duration: {{DESCRIPTION: reasoning about the task motion, forces, and other properties to determine an approximate time duration of the task, which must be positive}}.

Physical Model (if applicable):
- Relevant quantities and estimates: {{DESCRIPTION: include any relevant quantities and estimates used in the calculations}}.
- Relevant equations: {{DESCRIPTION: include any relevant equations used in the calculations}}.
- Relevant assumptions: {{DESCRIPTION: include any relevant assumptions made in the calculations}}.
- Computations: {{DESCRIPTION: include in full detail any relevant calculations using the above information}}.
- Force/torque motion computations with object of mass {{NUM}} kg and static friction coefficient of {{NUM}} along the surface: {{DESCRIPTION: for the derived or estimated motion, compute the force required to overcome friction and achieve the task}}.

Wrist Force/Torque Motion Estimation:
Linear X-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [positive, negative, no]}} force along the X-axis with magnitude {{PNUM}} N.
Linear Y-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [positive, negative, no]}} force along the Y-axis with magnitude {{PNUM}} N.
Linear Z-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: linear [positive, negative, no]}} force along the Z-axis with magnitude {{PNUM}} N.
Angular X-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the X-axis with magnitude {{PNUM}} N-m.
Angular Y-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Y-axis with magnitude {{PNUM}} N-m.
Angular Z-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Z-axis with magnitude {{PNUM}} N-m.
Grasping force:  {{DESCRIPTION: estimated force range and justification based on friction, mass, resistance}}, thus {{PNUM}} to {{PNUM}} N .

Python Code with Final Motion Plan:
```python
# succinct text description of the explicit estimated physical properties of the object, including mass, material, friction coefficients, etc.
property_description = "{{DESCRIPTION: describe succinctly the object and its properties}}"
# succinct text description of the motion plan along the wrist axes
wrist_motion_description = "{{DESCRIPTION: the object's required position motion in the wrist frame to accomplish the task}}"
# the vector (sign of direction * magnitude) of motion across the wrist axes [x, y ,z]. 
wrist_motion_vector = [{{NUM}}, {{NUM}}, {{NUM}}]
# the vector (sign of direction * magnitude) of the forces and torques along the wrist's [x, y, z, rx, ry, rz] axes
wrist_wrench = [{{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}]
# the grasping force, which must be positive
grasp_force = {{PNUM}}
# the task duration, which must be positive
duration = {{PNUM}}
```
[end of motion plan]

Rules:
1. Replace all {{DESCRIPTION: ...}}, {{PNUM}}, {{NUM}}, and {{CHOICE: ...}} entries with specific values or statements. For example, {{PNUM}} should be replaced with a number like 0.5. This is very important for downstream parsing!!
2. Use best physical reasoning based on known robot/environmental capabilities. Remember that the robot may have to exert forces in additional axes compared to the motion direction axes in order to maintain contacts between the object, robot, and environment.
3. Always include motion for all axes of motion, even if it's "No motion required."
4. Keep the explanation concise but physically grounded. Prioritize interpretability and reproducibility.
5. Use common sense where exact properties are ambiguous, and explain assumptions.
6. Do not include any sections outside the start/end blocks or add non-specified bullet points.
7. Make sure to provide the final python code for each requested force in a code block. Remember to fully replace the placeholder text with the actual values!
8. Do not abbreviate the prompt when generating the response. Fully reproduce the template, but filled in with your reasoning.
"""

wkspc_b_thinker = """
Given the user instruction and an image containing a third-person view of a robot and its environment, generate a structured physical plan for a robot end-effector interacting with the environment.
The task is to {task} while grasping the {obj}.

The robot is controlled using position and torque-based control, with access to contact feedback and 6D motion capabilities. 
Motions can include grasping, lifting, pushing, tapping, sliding, rotating, or any interaction with objects or surfaces.

Reason about the provided and implicit information in the images and task description to generate a structured plan for the robot's positional motion. Think about:
- Object geometry and contact points (from the image)
- Prior knowledge of object material types and mass estimates
- Force/torque sensing at the wrist
- Environmental knowledge (table, gravity, hinge resistance, etc.)

The image is a third-person view of the robot, labeled with the base robot coordinate frame placed at the point of grasping, which may be used to help with the mapping of the axes and understanding the environment
We must use the provided image data and physical reasoning to carefully map the true motion in the world frame to accomplish the task.
We want to reason about forces and torques relative to the world frame.

[start of motion plan]
The task is to {task} while grasping the {obj}.

Understanding Object-Centric Motion in the World Frame:
The provided images in the two-part image confirm {{DESCRIPTION: the object and environment in the image and their properties, such as color, shape, and material, and their correspondence to the requested task}}.
The blue axis representing the world Z-axis corresponds to upward (positive) and downward (negative) motion in the world. 
To complete the task, the object in the image should have {{CHOICE: [upward, downward, no]}} linear motion along the Z-axis with magnitude {{PNUM}} meters.
The red axis representing the world X-axis corresponds to right (positive) and left (negative) motion in the world, relative to the robot. 
To complete the task, the object in the image should have {{CHOICE: [leftward, rightward, no]}} linear motion along the X-axis with magnitude {{PNUM}} meters.
The green axis representing the world Y-axis corresponds to forward (positive) and backward (negative) motion in the world, relative to the robot. 
To complete the task, the object in the image should have {{CHOICE: [backward, forward, no]}} linear motion along the Y-axis with magnitude {{PNUM}} meters.
To accomplish the task in the world frame, the object must be moved {{DESCRIPTION: the object's required motion in the world frame to accomplish the task}}.

Understanding Robot-Applied Forces and Torques to Move Object in the World Frame:
To estimate the forces and torques required to accomplish {task} while grasping the {obj}, we must consider the following:
- Object Properties: {{DESCRIPTION: Think very carefully about the estimated mass, material, stiffness, friction coefficient of the object based off the visual information and semantic knowledge about the object. If object is articulated, do the same reasoning for whatever joint / degree of freedom enables motion. }}.
- Environmental Factors: {{DESCRIPTION: Think very carefully about the various environmental factors in task like gravity, surface friction, damping, hinge resistance that would interact with the object over the course of the task}}.
- The relevant object is {{DESCRIPTION: describe the object and its properties}} has mass {{NUM}} kg and, with the robot gripper, has a static friction coefficient of {{NUM}}.
- The surface of interaction is {{DESCRIPTION: describe the surface and its properties}} has a static friction coefficient of {{NUM}} with the object.
- Contact Types: {{DESCRIPTION: consideration of various contacts such as edge contact, maintaining surface contact, maintaining a pinch grasp, etc.}}.
- Motion Type: {{DESCRIPTION: consideration of forceful motion(s) involved in accomplishing task such as pushing forward while pressing down, rotating around hinge by pulling up and out, or sliding while maintaining contact}}.
- Contact Considerations: {{DESCRIPTION: explicitly consider whether additional axes of force are required to maintain contact with the object, robot, and environment and accomplish the motion goal}}.
- Motion along axes: {{DESCRIPTION: e.g., the robot exerts motion in a “linear,” “rotational,” “some combination” fashion along the [x, y, z, rx, ry, rz] axes}}.
- Task duration: {{DESCRIPTION: reasoning about the task motion, forces, and other properties to determine an approximate time duration of the task, which must be positive}}.

Physical Model Computations:
- Relevant quantities and estimates: {{DESCRIPTION: include any relevant quantities and estimates used in the calculations}}.
- Relevant equations: {{DESCRIPTION: include any relevant equations used in the calculations}}.
- Relevant assumptions: {{DESCRIPTION: include any relevant assumptions made in the calculations}}.
- Computations: {{DESCRIPTION: include in full detail any relevant calculations using the above information}}.
- Grasping force computations: {{DESCRIPTION: typically, using the estimated mass m and estimated gripper-object friction mu, a good grasping force is (m*g)/mu. Use this calculation first and only modify it if deemed appropriate}}.
- Force/torque motion computations with object of mass {{NUM}} kg and static friction coefficient of {{NUM}} along the surface: {{DESCRIPTION: for the derived or estimated motion, compute the force required to overcome friction and achieve the task}}.

Force/Torque Motion Estimation:
Linear X-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [leftward, rightward, no]}} force along the X-axis with magnitude {{PNUM}} N.
Linear Y-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [backward, forward, no]}} force along the Y-axis with magnitude {{PNUM}} N.
Linear Z-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: linear [upward, downward, no]}} force along the Z-axis with magnitude {{PNUM}} N.
Angular X-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the X-axis with magnitude {{PNUM}} N-m.
Angular Y-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Y-axis with magnitude {{PNUM}} N-m.
Angular Z-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Z-axis with magnitude {{PNUM}} N-m.
Grasping force:  {{DESCRIPTION: estimated force range and justification based on friction, mass, resistance}}, thus {{PNUM}} to {{PNUM}} N .

Python Code with Final Motion Plan:
```python
# succinct text description of the explicit estimated physical properties of the object, including mass, material, friction coefficients, etc.
property_description = "{{DESCRIPTION: describe succinctly the object and its properties}}"
# succinct text description of the motion plan along the world axes
world_motion_description = "{{DESCRIPTION: the object's required position motion in the world frame to accomplish the task}}"
# the vector (sign of direction * magnitude) of motion across the motion direction axes [x, y ,z]. 
world_motion_vector = [{{NUM}}, {{NUM}}, {{NUM}}]
# the vector (sign of direction * magnitude) of the forces and torques along the [x, y, z, rx, ry, rz] axes
ft_vector = [{{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}]
# the grasping force, which must be positive
grasp_force = {{PNUM}}
# the task duration, which must be positive
duration = {{PNUM}}
```
[end of motion plan]

Rules:
1. Replace all {{DESCRIPTION: ...}}, {{PNUM}}, {{NUM}}, and {{CHOICE: ...}} entries with specific values or statements. For example, {{PNUM}} should be replaced with a number like 0.5. This is very important for downstream parsing!!
2. Use best physical reasoning based on known robot/environmental capabilities. Remember that the robot may have to exert forces in additional axes compared to the motion direction axes in order to maintain contacts between the object, robot, and environment.
3. Always include motion for all axes of motion, even if it's "No motion required."
4. Keep the explanation concise but physically grounded. Prioritize interpretability and reproducibility.
5. Use common sense where exact properties are ambiguous, and explain assumptions.
6. Do not include any sections outside the start/end blocks or add non-specified bullet points.
7. Make sure to provide the final python code for each requested force in a code block. Remember to fully replace the placeholder text with the actual values!
8. Do not abbreviate the prompt when generating the response. Fully reproduce the template, but filled in with your reasoning.
9. Make sure to refer to the provided correspondence in the direction guide between motion in the world frame and positive/negative motion in the respective axes.
"""

wb_3b_thinker = """
Given the user instruction and two-part image containing a robot wrist-image view on the left, a third-person view on the right, generate a structured physical plan for a robot end-effector interacting with the environment.
The task is to {task} while grasping the {obj}.

The robot is controlled using position and torque-based control, with access to contact feedback and 6D motion capabilities. 
Motions can include grasping, lifting, pushing, tapping, sliding, rotating, or any interaction with objects or surfaces.

Reason about the provided and implicit information in the images and task description to generate a structured plan for the robot's positional motion. Think about:
- Object geometry and contact points (from the image)
- Prior knowledge of object material types and mass estimates
- Force/torque sensing at the wrist
- Environmental knowledge (table, gravity, hinge resistance, etc.)

The left image is a robot-wrist view labeled with the axes of motion relative to the base robot coordinate frame, placed at the point of, as in the canonical world-axes (for example, the red positive Z-axis will always represent upward direction in the world).
The right image is a third-person view of the robot, which may be used to help with the mapping of the axes and understanding the environment
We must use the provided image data and physical reasoning to carefully map the true motion in the world frame to accomplish the task.
We want to reason about forces and torques relative to the world frame.

[start of motion plan]
The task is to {task} while grasping the {obj}.

Understanding Object-Centric Motion in the World Frame:
The provided images in the two-part image confirm {{DESCRIPTION: the object and environment in the image and their properties, such as color, shape, and material, and their correspondence to the requested task}}.
The blue axis representing the world Z-axis corresponds to upward (positive) and downward (negative) motion in the world. 
To complete the task, the object in the image should have {{CHOICE: [upward, downward, no]}} linear motion along the Z-axis with magnitude {{PNUM}} meters.
The red axis representing the world X-axis corresponds to right (positive) and left (negative) motion in the world, relative to the robot. 
To complete the task, the object in the image should have {{CHOICE: [leftward, rightward, no]}} linear motion along the X-axis with magnitude {{PNUM}} meters.
The green axis representing the world Y-axis corresponds to forward (positive) and backward (negative) motion in the world, relative to the robot. 
To complete the task, the object in the image should have {{CHOICE: [backward, forward, no]}} linear motion along the Y-axis with magnitude {{PNUM}} meters.
To accomplish the task in the world frame, the object must be moved {{DESCRIPTION: the object's required motion in the world frame to accomplish the task}}.

Understanding Robot-Applied Forces and Torques to Move Object in the World Frame:
To estimate the forces and torques required to accomplish {task} while grasping the {obj}, we must consider the following:
- Object Properties: {{DESCRIPTION: Think very carefully about the estimated mass, material, stiffness, friction coefficient of the object based off the visual information and semantic knowledge about the object. If object is articulated, do the same reasoning for whatever joint / degree of freedom enables motion. }}.
- Environmental Factors: {{DESCRIPTION: Think very carefully about the various environmental factors in task like gravity, surface friction, damping, hinge resistance that would interact with the object over the course of the task}}.
- The relevant object is {{DESCRIPTION: describe the object and its properties}} has mass {{NUM}} kg and, with the robot gripper, has a static friction coefficient of {{NUM}}.
- The surface of interaction is {{DESCRIPTION: describe the surface and its properties}} has a static friction coefficient of {{NUM}} with the object.
- Contact Types: {{DESCRIPTION: consideration of various contacts such as edge contact, maintaining surface contact, maintaining a pinch grasp, etc.}}.
- Motion Type: {{DESCRIPTION: consideration of forceful motion(s) involved in accomplishing task such as pushing forward while pressing down, rotating around hinge by pulling up and out, or sliding while maintaining contact}}.
- Contact Considerations: {{DESCRIPTION: explicitly consider whether additional axes of force are required to maintain contact with the object, robot, and environment and accomplish the motion goal}}.
- Motion along axes: {{DESCRIPTION: e.g., the robot exerts motion in a “linear,” “rotational,” “some combination” fashion along the [x, y, z, rx, ry, rz] axes}}.
- Task duration: {{DESCRIPTION: reasoning about the task motion, forces, and other properties to determine an approximate time duration of the task, which must be positive}}.

Physical Model Computations:
- Relevant quantities and estimates: {{DESCRIPTION: include any relevant quantities and estimates used in the calculations}}.
- Relevant equations: {{DESCRIPTION: include any relevant equations used in the calculations}}.
- Relevant assumptions: {{DESCRIPTION: include any relevant assumptions made in the calculations}}.
- Computations: {{DESCRIPTION: include in full detail any relevant calculations using the above information}}.
- Grasping force computations: {{DESCRIPTION: typically, using the estimated mass m and estimated gripper-object friction mu, a good grasping force is (m*g)/mu. Use this calculation first and only modify it if deemed appropriate}}.
- Force/torque motion computations with object of mass {{NUM}} kg and static friction coefficient of {{NUM}} along the surface: {{DESCRIPTION: for the derived or estimated motion, compute the force required to overcome friction and achieve the task}}.

Force/Torque Motion Estimation:
Linear X-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [leftward, rightward, no]}} force along the X-axis with magnitude {{PNUM}} N.
Linear Y-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: [backward, forward, no]}} force along the Y-axis with magnitude {{PNUM}} N.
Linear Z-axis:  To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: linear [upward, downward, no]}} force along the Z-axis with magnitude {{PNUM}} N.
Angular X-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the X-axis with magnitude {{PNUM}} N-m.
Angular Y-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Y-axis with magnitude {{PNUM}} N-m.
Angular Z-axis: To complete the task and based upon {{DESCRIPTION: reasoning about and estimation of task physical properties}}, the robot must exert on the object in the image {{CHOICE: angular [counterclockwise, clockwise, no]}} torque about the Z-axis with magnitude {{PNUM}} N-m.
Grasping force:  {{DESCRIPTION: estimated force range and justification based on friction, mass, resistance}}, thus {{PNUM}} to {{PNUM}} N .

Python Code with Final Motion Plan:
```python
# succinct text description of the explicit estimated physical properties of the object, including mass, material, friction coefficients, etc.
property_description = "{{DESCRIPTION: describe succinctly the object and its properties}}"
# succinct text description of the motion plan along the world axes
world_motion_description = "{{DESCRIPTION: the object's required position motion in the world frame to accomplish the task}}"
# the vector (sign of direction * magnitude) of motion across the motion direction axes [x, y ,z]. 
world_motion_vector = [{{NUM}}, {{NUM}}, {{NUM}}]
# the vector (sign of direction * magnitude) of the forces and torques along the [x, y, z, rx, ry, rz] axes
ft_vector = [{{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}, {{NUM}}]
# the grasping force, which must be positive
grasp_force = {{PNUM}}
# the task duration, which must be positive
duration = {{PNUM}}
```
[end of motion plan]

Rules:
1. Replace all {{DESCRIPTION: ...}}, {{PNUM}}, {{NUM}}, and {{CHOICE: ...}} entries with specific values or statements. For example, {{PNUM}} should be replaced with a number like 0.5. This is very important for downstream parsing!!
2. Use best physical reasoning based on known robot/environmental capabilities. Remember that the robot may have to exert forces in additional axes compared to the motion direction axes in order to maintain contacts between the object, robot, and environment.
3. Always include motion for all axes of motion, even if it's "No motion required."
4. Keep the explanation concise but physically grounded. Prioritize interpretability and reproducibility.
5. Use common sense where exact properties are ambiguous, and explain assumptions.
6. Do not include any sections outside the start/end blocks or add non-specified bullet points.
7. Make sure to provide the final python code for each requested force in a code block. Remember to fully replace the placeholder text with the actual values!
8. Do not abbreviate the prompt when generating the response. Fully reproduce the template, but filled in with your reasoning.
9. Make sure to refer to the provided correspondence in the direction guide between motion in the world frame and positive/negative motion in the respective axes.
"""