
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 rectangular prism has 6 faces (2 rectangular and 4 square faces), 12 edges, and 8 vertices. Choose one of its square faces as the base of a new pyramid. The numbers of external faces, vertices, and edges of the resulting shape (the combination of the prism and pyramid) are added. What is the maximum value of this sum?

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