
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 the top face. The cube is placed on a flat surface and begins to roll along one of its edges without slipping or lifting, such that at least two of its vertices are always in contact with the surface. The rolling continues until the cube completes a full cycle and the dot is at the top face again. Calculate the length of the path followed by the dot throughout this motion, expressed as $k\pi$, where $k$ is a constant to be determined.

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