
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 of size $5 \times 5 \times 5$, divided each face into unit squares, and painted each of these squares in one of three colors - black, white, or red - such that no two adjacent squares share the same color. What is the minimum number of black squares that could result? (Squares that share a common side 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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