
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 cube where all 8 vertices are linked such that each vertex connects directly to 3 other vertices. First, an ant starts at one vertex on the top face of the cube and randomly selects and moves to one of the three adjacent vertices, which it names vertex A. From vertex A, the ant then randomly selects one of the three vertices adjacent to vertex A (excluding the vertex it came from) and moves to it, calling this vertex B. What is the probability that vertex B is one of the bottom face vertices? Express your answer as a common fraction.

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