
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 an edge length of 2 cm has a dot marked at the center of one of its side faces, not the top face. The cube is placed on a flat table, and it is rolled in one direction so that at least two of its vertices always touch the table. The cube completes a full rotation to return to its initial position with the marked face on top. Calculate the length, in centimeters, of the path followed by the dot during this full rotation, expressed in the form $k\pi$, where $k$ is a constant to be determined.

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