
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
Given that Erin the ant starts at one vertex of a regular tetrahedron and crawls along exactly 3 edges in such a way that she visits every vertex exactly once without revisiting any vertex or repeating any edge, determine the number of distinct paths Erin can take.

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