
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
An abstract artist took a wooden cube measuring 5×5×5, divided each face into unit squares, and painted each of them in one of three colors - black, white, or red - such that no two squares sharing an edge have the same color. What is the smallest number of black squares that could result? (Squares sharing an edge are considered adjacent even if they are on different faces of the cube.)

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