
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
Imagine a cube where an ant starts at the top vertex and randomly selects one of the four adjacent vertices (call this vertex A). From vertex A, the ant again randomly selects one of the adjacent vertices (call this vertex B). From vertex B, the ant randomly selects one of the adjacent vertices to end its walk (call this vertex C). What is the probability that vertex C will be the bottom vertex of the cube, directly opposite the starting top vertex? Express your answer as a common fraction.

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