
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
Consider a dodecahedron, where each face is a regular pentagon. An ant starts at one vertex and moves to one of the three adjacent vertices, which it selects randomly and calls vertex A. From vertex A, the ant moves to one of the three adjacent vertices, randomly selecting it and calling it vertex B. What is the probability that vertex B is on the opposite pentagonal face relative to the starting vertex? Express your answer as a common fraction.

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