
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
Consider:
\begin{eqnarray*}
&(1)& x\text{ and }y\text{ are both integers between 100 and 999, inclusive;}\qquad \qquad \qquad \qquad \qquad \\
&(2)& y\text{ is the number formed by reversing the digits of }x\text{; and}\\
&(3)& z=|x-y|.
\end{eqnarray*}
Assume the digits $a$ or $c$ (first or last digits of $x$, respectively) could be zero. How many distinct values of $z$ are possible?

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