
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
Infinite repeating decimals are rational numbers, such as: $0.\overline{1}$, $0.\overline{2}$, $0.\overline{3}$, ... Observing $0.\overline{1}= \frac{1}{9}$, $0.\overline{2}= \frac{2}{9}$, $0.\overline{3}= \frac{1}{3}$, ..., we can induce that $0.\overline{23}=\_\_\_\_\_\_\_\_$.

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