
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 positive integer  $n (n>2004)$ , we put 1, 2, 3, …, $n^2$  into squares of an  $n\times n$  chessboard with one number in a square. A square is called a “good square” if the square satisfies following conditions:
1) There are at least 2004 squares that are in the same row with the square such that any number within these 2004 squares is less than the number within the square.
2) There are at least 2004 squares that are in the same column with the square such that any number within these 2004 squares is less than the number within the square.
Find the maximum value of the number of the “good square”.

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