
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 rectangular prism is used as the base for a new pyramid. The numbers of exterior faces, vertices, and edges of the resulting shape (the combination of the prism and pyramid) are added together. What is the maximum value of this sum?

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