
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 4x4x4 cube is formed by assembling 64 unit cubes. Three large squares are painted on each of the six faces of the cube according to the pattern shown, where the squares are arranged to cover the four corners on each face. How many of the 64 unit cubes have no paint on them?

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