
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

Given a $1000 \times 1000$ grid, a cheetah placed on any cell $x$ attacks all cells within a $19 \times 19$ square centered on $x$, except for the cells that are in the same row or column as $x$. What is the maximum number of cheetahs that can be placed on the grid such that no two cheetahs attack each other?

(I. Bogdanov)

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