
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 rectangular prism with dimensions 2 cm by 2 cm by 1 cm has a dot marked in the center of the top face. It sits on a flat table with the face of dimensions 2 cm by 1 cm on the table. The prism is rolled in one direction, touching at least two of its vertices on the table at all times, until the dot is again on the top face. The length of the path followed by the dot is $c\pi$, where $c$ is a constant. What is $c$?

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