
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. Each of the six faces of the cube has a cross pattern painted on it, where the middle four unit squares and one additional unit square extending along each direction from the middle form the pattern, totaling $10$ painted unit squares on each face. 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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