
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
Misha has a \(7 \times 7\) square of paper, and all its cells are white. Misha wants to color \(N\) cells black. What is the smallest \(N\) such that after coloring, it would be impossible to cut out any completely white rectangle with at least ten cells from the square?

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