
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 \(x\).
3. \(z = |x - y|\).
How many distinct values of \(z\) are possible?

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