
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
For a four-digit number $n$, with each digit not being $0$, if the sum of the thousands digit and the tens digit of $n$ is equal to the sum of the hundreds digit and the units digit, then $n$ is called an "equal sum number." By exchanging the thousands digit and the tens digit of the "equal sum number" $n$, and exchanging the hundreds digit and the units digit, we obtain a new "equal sum number" $n'$, where $F(n)=\frac{n+n'}{101}$ and $G(n)=\frac{n-n'}{99}$. For example, if $n=1342$ and $n'=4213$, then $F(1342)=\frac{1342+4213}{101}=55$ and $G(1342)=\frac{1342-4213}{99}=-29$. Calculate $F(5236)-G(5236)=$____; when $\frac{F(n)}{13}$ and $\frac{G(n)}{7}$ are both integers, the maximum value of $n$ is ____.

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