
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 one of its faces. The cube rests on a flat surface and is rolled in one direction so that at least two of its vertices are always in contact with the surface. The cube completes a sequence of rolls until the dot returns to the top position. Calculate the length, in centimeters, of the path followed by the dot, expressed as $d\pi$, where $d$ is a constant.

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