
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 made up of 216 unit cubes. On each face of the cube, only the central 2x2 square is painted. Determine how many of the 216 unit cubes remain without any paint.

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