
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 6x6x6 cube is formed by assembling 216 unit cubes. Sixteen unit squares are painted on each of the two opposite faces of the cube, and nine unit squares are painted on each of the other four faces. How many of the 216 unit cubes have no paint on them?

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