
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 edge length \( n \) (where \( n > 2 \) and \( n \in \mathbf{N} \)) is entirely painted black on its surface. The cube is then divided into \( n^{3} \) smaller cubes, each with edge length 1. If the number of smaller cubes that have exactly one face painted black is equal to the number of smaller cubes that have no faces painted black, determine the value of \( n \).

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