
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 an octahedron formed by two square-based pyramids glued together along their bases. An ant starts at the top vertex and makes three sequential random moves to adjacent vertices, labeling them sequentially as vertex A, B, and C. After reaching vertex C, what is the probability that this vertex C is the bottom vertex of the octahedron? Express your answer as a common fraction.

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