
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 with integer edge lengths is fully painted red on its surface. It is then cut into smaller cubes with edge lengths of 1. Among these smaller cubes, 40 have paint on two faces, and 66 have paint on one face. What is the volume of this rectangular prism?

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