
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 4 cm has a dot marked in the center of the top face when it rests on one of its 2 cm faces on a flat table. The prism is rolled, without lifting or slipping, along its length so that at least two of its vertices are always touching the table. The prism is rolled until the dot is again on the top face (originally 2x4 cm face). The length, in centimeters, of the path followed by the dot is $c\pi$, where $c$ is a constant. Determine the value of $c$.

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