
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, which is made up of 12 pentagonal faces. An ant starts at one of the top vertices and walks to one of the three adjacent vertices (vertex A). From vertex A, the ant walks again to one of its adjacent vertices (vertex B). What is the probability that vertex B is one of the bottom vertices? There are three bottom vertices in total in a dodecahedron.

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