
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. A 'plus' shaped pattern with 13 unit squares is painted on each of the six faces of the cube. How many of the 216 unit cubes have no paint on them? The plus shape covers one central square and extends out by one unit in each direction along the face of the cube.

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