
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
Principal Skinner is thinking of two integers  $m$  and  $n$  and bets Superintendent Chalmers that he will not be able to determine these integers with a single piece of information.  Chalmers asks Skinner the numerical value of  $mn+13m+13n-m^2-n^2$ .  From the value of this expression alone, he miraculously determines both  $m$  and  $n$ .  What is the value of the above expression.

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