
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 1 cm by 1 cm has a dot marked in the centre of the top face. The prism is placed on a flat table with the 2 cm by 1 cm face as the base. The prism is rolled, without lifting or slipping, along its longer side so that at least two of its vertices are always touching the table. The prism is rolled until the dot completes two full revolutions and ends up, yet again, on the top face in the same spot from where it started. The length, in centimeters, of the path followed by the dot is $k\pi$, where $k$ is a constant. What is $k$?

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