
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
Each square of a  $7 \times 8$  board is painted black or white, in such a way that each  $3 \times 3$  subboard has at least two black squares that are neighboring. What is the least number of black squares that can be on the entire board?

Clarification: Two squares are *neighbors* if they have a common side.

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