
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 hundreds, tens, and units digits of a three-digit number are denoted as $x$, $y$, and $z$ respectively, then this three-digit number can be represented as $\overline{xyz}$, and it is easy to see that $\overline{xyz} = 100x + 10y + z. \ (1)$ If we want to form a three-digit number using the digits $3$, $7$, and $9$ (with distinct digits in each place), then the largest three-digit number that can be formed is ______, and the smallest three-digit number that can be formed is ______. <br/> $(2)$ If a three-digit number is composed of the digits $a$, $b$, and $c$, where $a > b > c > 0$, then please explain why the difference between the largest and smallest three-digit numbers that can be formed is divisible by $99$.

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