
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 edge length 2 cm has a dot exactly in the center of one of its faces. The cube rests on a table and is rolled over its edges in such a way that each face eventually returns to the top position once without slipping or lifting. Determine the length of the path traced by the dot in terms of $d\pi$, where $d$ is a constant.

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