
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 a $n \times n \times n$ cube, completely white on the outside. What is the minimum number of cube faces Vasya has 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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