
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 new pyramid is added on one of the pentagonal faces of a pentagonal prism. Calculate the total number of exterior faces, vertices, and edges of the composite shape formed by the fusion of the pentagonal prism and the pyramid. What is the maximum value of this sum?

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