
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 assembled from 64 unit cubes. Only one unit square on each of the six faces of the cube is painted. 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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