
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
The sum of the numbers in each row of a 5-by-5 square must be the same as the sum of the numbers in each column, and the sum of the numbers in the main diagonals, given a set of 25 integers from -12 to 12, inclusive. Calculate the common sum of the 5 rows, which is equal to the common sum of the 5 columns, and the common sum of each of the main diagonals.

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