
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
The recurring decimal \(0 . \dot{x} y \dot{z}\), where \(x, y, z\) denote digits between 0 and 9 inclusive, is converted to a fraction in lowest term. How many different possible values may the numerator take?

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