
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
Assume:
1. \(x\) and \(y\) are integers such that \(100 \leq x, y \leq 555\),
2. \(y\) is the number formed by reversing the digits of \(x\),
3. \(z = 2|x - y|\).

Determine how many distinct values \(z\) can have.

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