
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 edges of length 2 cm has a dot marked in the center of the top face. The cube is rolled, without lifting or slipping, along a flat table in one direction, such that at least two of its vertices are always touching the table. The cube is rolled until the dot returns to the top face. Determine the length, in centimeters, of the path followed by the dot, expressed in the form \(c\pi\), where \(c\) is a constant.

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