
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A cube with edge length 2 cm is sitting on a flat table along with a sphere of radius 1 cm. Both are initially positioned so their centers are at the same height. A dot is marked at the center of the top face of the cube. Both the cube and the sphere are rolled forward in the same direction without slipping until each one makes a complete revolution and the dot returns to the top face of the cube. Find the length, in centimeters, of the path followed by the dot, expressed as $d\pi$, where $d$ is a constant.

Present the answer in LaTex format: \boxed{Your answer}
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