
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 a $N \times N$ square table, all integers are arranged according to the following rule: 1 is placed in any cell, 2 is placed in the row whose number is equal to the column number containing 1, 3 is placed in the row whose number is equal to the column number containing 2, and so on. By how much does the sum of the numbers in the column containing $N^{2}$ differ from the sum of the numbers in the row containing 1?

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