
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 0 and 999, inclusive;
2. \(y\) is the number formed by reversing the digits of \(x\);
3. \(z = |x - y|\).

Determine how many distinct values of \(z\) are possible.

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