
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
Let the units digit of a two-digit number be $a$ and the tens digit be $b$ ($a$ and $b$ are positive integers, and $a \gt b$). If the positions of the units and tens digits of this two-digit number are swapped to form a new two-digit number, then the difference between the new two-digit number and the original two-digit number must be a multiple of $9$. Explain the reason.

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