
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 triangular pyramid, all edges of which have a length of 6 cm, stands on a flat table. The pyramid is rolled across the table over its edges 6 times such that one of its vertices remains stationary all the time, and the pyramid is not rolled over the same edge twice in a row. Find the length of the trajectory along which the moving vertex of the pyramid travels during these rolls.

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