
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 regular tetrahedron with edge length 2 cm has a dot marked in the centre of one of its faces. It is sitting on a flat table. The tetrahedron is rolled, without lifting or slipping, over its edges so that at least two of its vertices are always touching the table. The tetrahedron is rolled until the dot is again on the top face. The length, in centimeters, of the path followed by the dot is $d\pi$, where $d$ is a constant. What is $d$?

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