
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 six faces of a cube will be used as the base of a new pyramid. Calculate the maximum value of the sum of the number of exterior faces, vertices, and edges of the resulting shape after fusing the cube and pyramid.

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