
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 cube with an edge length of \( n \) (where \( n \) is a positive integer) is painted red on its surface and then cut into \( n^3 \) smaller cubes with an edge length of 1. It is found that the number of small cubes with only one face painted red is exactly 12 times the number of small cubes with two faces painted red. Find the value of \( n \).

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