
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 at their bases. An ant starts from the top vertex and walks to one of the four adjacent vertices, denoted as vertex A. From vertex A, it randomly walks to one of the four adjacent vertices, denoted as vertex B. From vertex B, it then walks to one of the four adjacent vertices, denoted as vertex C. Find the probability that vertex C is either the original top vertex or the bottom vertex.

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