
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 truncated pyramid formed by slicing the top off a regular pyramid. The larger base now has 6 vertices, and the smaller top base is a regular hexagon. The ant starts at the top vertex of the truncated pyramid, walks randomly to one of the six adjacent vertices on the larger base, and then from there, it walks to one of the six adjacent vertices on the smaller top base. What is the probability that this final vertex is the initially started top vertex? Express your answer as a common fraction.

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