
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 square pyramid is added to one of the faces of a rectangular prism, which consists of 6 faces, 12 edges, and 8 vertices. Calculate the maximum possible sum of the number of exterior faces, vertices, and edges of the resulting solid when the pyramid is added to different faces of the prism.

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