
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 triangular prism with 5 faces, 9 edges, and 6 vertices is extended by attaching a regular pentagonal prism at one of its quadrilateral faces. One of the pentagonal faces of this new extended shape will be used as the base of a new pyramid. Determine the maximum value of the sum of the exterior faces, vertices, and edges of the resulting composite shape after adding the pyramid.

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