
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
If the sum of the units digit, tens digit, and hundreds digit of a four-digit number $M$ is $12$, then this four-digit number $M$ is called an "eternal number." By swapping the thousands digit and hundreds digit of the "eternal number" $M$, and swapping the tens digit and units digit, we obtain a new four-digit number $N$. Let $F(M)=\frac{{M-N}}{9}$. If the difference between the hundreds digit and units digit of an "eternal number" $M$ is exactly the thousands digit, and $\frac{{F(M)}}{9}$ is an integer, then the maximum value of $F(M)$ is ____.

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