
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 has edges of length 2 cm and has a dot marked in the center of the top face. The cube is placed on a flat table. The cube is rolled in one direction such that at least two of its vertices always touch the table. It is rolled until the dot appears twice on the top face, after making several complete cycles on the surfaces of the cube. Calculate the length, in centimeters, of the pathway followed by the dot in terms of $c\pi$, where $c$ is a constant. What is $c$?

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