
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 side length 2 cm has a dot marked at a point one-third away from one edge on the top face. This cube, placed on a flat table, is rolled (without lifting or slipping) in one direction, maintaining at least two of its vertices always touching the table. The cube is rolled until the dot is on the top face again. Calculate the length, in centimeters, of the path followed by the dot in terms of $\pi$.

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