
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
A modified octahedron consists of two pyramids, each with a pentagonal base, glued together along their pentagonal bases, forming a polyhedron with twelve faces. An ant starts at the top vertex and walks randomly to one of the five adjacent vertices in the middle ring. From this vertex, the ant walks again to another randomly chosen adjacent vertex among five possibilities. What is the probability that the second vertex the ant reaches is the bottom vertex of the polyhedron? Express your answer as a common fraction.

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