
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 icosahedron, a polyhedron with 20 faces, each being an equilateral triangle. An ant starts at one of the vertices at the top of the icosahedron and can walk to one of the five adjacent vertices. From the new vertex it reaches, called vertex A, the ant randomly selects one of its five adjacent vertices, called vertex B. What is the probability that vertex B is the opposite vertex to the starting vertex? Assume the icosahedron is positioned such that there are direct opposite vertices vertically aligned.

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