
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
Suppose each face of a regular tetrahedron is painted with a narrow stripe from the center of one vertex to the midpoint of the opposite edge. The choice of midpoint for each face is made randomly. What is the probability that there is a continuous stripe reconnecting to its starting point, without crossing over itself?
A) $\frac{1}{81}$
B) $\frac{1}{27}$
C) $\frac{1}{9}$
D) $\frac{1}{3}$

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