
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 square grid with a side length of 1000, what is the maximum number of cells that can be colored black so that it is not possible to find three black cells where two are in the same row and two are in the same column?

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