
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
Given that
1. $x$ and $y$ are both integers between 100 and 999, inclusive;
2. $y$ is the number formed by swapping the hundreds and tens digits of $x$, the units digit remains the same;
3. $z = |x - y|$.
How many distinct values of $z$ are possible?

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