
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. On each face of the cube, two strips of three unit squares are painted, running parallel to the sides of the face, one unit away from the center line (on both sides). Each strip is 1 unit wide and spans the entire edge length of the face. How many of the 216 unit cubes have no paint on them?

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