
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
Observe the following equations about converting repeating decimals to fractions: (Note: the numbers with dots on top) $0.\dot{3} = \frac{3}{9} = \frac{1}{3}$, $1.\dot{1}\dot{8} = \frac{18}{99} = \frac{2}{11}$, $0.\dot{3}\dot{5}\dot{2} = \frac{352}{999}$, $0.000\dot{5}\dot{9} = \frac{1}{1000} \times \frac{59}{99} = \frac{59}{99000}$. Based on this, infer the fraction form of the repeating decimal $0.2\dot{3}$.

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