
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 cell of a $10 \times 10$ board is painted either black or white. A cell is said to be "not in its place" if it has at least seven neighbors of a different color than itself. (Neighbors are cells that share a common side or a common corner.) What is the maximum number of cells on the board that can simultaneously be "not in their place"?

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