
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 face of a regular tetrahedron is given a single narrow stripe painted from one vertex to the opposite vertex. The choice of the vertex pairing is made at random and independently for each face. Calculate the probability that there is a continuous stripe connecting all vertices.

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