
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
Each edge of a regular tetrahedron is given a stripe. The choice of which edge to stripe is made at random. What is the probability that there is at least one triangle face with all its edges striped?

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