
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
One of the eight faces of a hexagonal prism will be transformed into the base of a new pyramid. Calculate the maximum sum of the number of exterior faces, vertices, and edges of the resultant composite shape (combining the prism and pyramid) when the pyramid is added to each type of face of the prism.

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