
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 is sitting on a flat surface and rolls over its edges to make exactly four quarter-turns (90 degrees each), without slipping, until the dot is back on the same face, initially facing up. Calculate the length, in centimeters, of the path followed by the dot. The path's length is expressed as $k\pi$, where $k$ is a constant. Determine the value of $k$.

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