
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
Fill in the integers \(1, 2, 3, \ldots, 2016^2\) into a \(2016 \times 2016\) grid, with each cell containing a unique number. Draw a vector from the center of one cell to the center of another if the number in the first cell is smaller than the number in the second cell. If the sum of the numbers in each row and each column of the grid is the same, find the sum of all the vectors drawn.

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