
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 marked in the center of the top face. The cube is placed on a flat surface and is rolled over its edges in a specific sequence without lifting or slipping, such that during the initial roll, one vertex remains in contact with the surface. The cube completes one full cycle of motion until the dot is again on the top face. Find the length of the path followed by the dot in terms of $\pi$.

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