
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 a modified octahedron with an additional layer of four vertices between the middle ring and the bottom vertex, making the structure more like a double pyramid with three layers. The top vertex connects to the four vertices in the first middle layer, each vertex in the first middle layer connects directly to another set of four vertices in the second middle layer, and all vertices in the second middle layer connect to the bottom vertex. An ant starts at the top vertex, randomly moves to one of the four vertices in the first middle layer (vertex A), then randomly moves to one of the four vertices directly connected to the vertex A in the second middle layer (vertex B), and finally moves to one of the five vertices (four from the second middle layer plus the bottom vertex) adjacent to vertex B. What is the probability that the ant's final destination will be the bottom vertex? Express your answer as a common fraction.

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