
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 \( n^2 \) distinct real numbers arranged in an \( n \times n \) table, extract the maximum number from each column and the minimum number from each row. Find the number of ways to arrange \( 2n \) distinct numbers so that they can be extracted exactly in this manner.

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