
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
On a $25 \times 25$ grid of white cells, several cells are colored black such that exactly 9 cells in each row and each column are black. What is the smallest number $k$ of cells that must be recolored white to ensure that it is impossible to cut out a $2 \times 2$ black square?

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