
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
Some squares of a  $1999\times 1999$  board are occupied with pawns. Find the smallest number of pawns for which it is possible that for each empty square, the total number of pawns in the row or column of that square is at least  $1999$ .

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