
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
Petya has $n^{3}$ white $1 \times 1 \times 1$ cubes. He wants to assemble them into an $n \times n \times n$ cube that is completely white on the outside. What is the minimum number of cube faces Vasya needs to paint to prevent Petya from achieving this? Solve the problem for a) $n=2$; b) $n=3$.

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