
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
There are 6 rectangular prisms with edge lengths of \(3 \text{ cm}\), \(4 \text{ cm}\), and \(5 \text{ cm}\). The faces of these prisms are painted red in such a way that one prism has only one face painted, another has exactly two faces painted, a third prism has exactly three faces painted, a fourth prism has exactly four faces painted, a fifth prism has exactly five faces painted, and the sixth prism has all six faces painted. After painting, each rectangular prism is divided into small cubes with an edge length of \(1 \text{ cm}\). What is the maximum number of small cubes that have exactly one red face?

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