
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 pentagonal prism is used as the base of a new pyramid. One of the seven faces of this pentagonal prism will be chosen as the base of the pyramid. Calculate the maximum value of the sum of the exterior faces, vertices, and edges of the resulting structure after this pyramid is added.

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