
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
Define: For any three-digit natural number $m$, if $m$ satisfies that the tens digit is $1$ greater than the hundreds digit, and the units digit is $1$ greater than the tens digit, then this three-digit number is called an "upward number"; for any three-digit natural number $n$, if $n$ satisfies that the tens digit is $1$ less than the hundreds digit, and the units digit is $1$ less than the tens digit, then this three-digit number is called a "downward number." The multiple of $7$ of an "upward number" $m$ is denoted as $F(m)$, and the multiple of $8$ of a "downward number" $n$ is denoted as $G(n)$. If $\frac{F(m)+G(n)}{18}$ is an integer, then each pair of $m$ and $n$ is called a "seven up eight down number pair." In all "seven up eight down number pairs," the maximum value of $|m-n|$ is ______.

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