
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
In an \(N \times N\) table, all natural numbers from 1 to \(N^2\) are arranged. A number is called "big" if it is the largest in its row and "small" if it is the smallest in its column (thus, a number can be both big and small, or neither). Find the smallest possible difference between the sum of all big numbers and the sum of all small numbers.

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