
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
Given an infinite geometric sequence $\{a\_n\}$ (with an infinite number of terms) where $|q| < 1$ (with $q$ being the common ratio), we define the sum of its terms, denoted as $S$, to be the limit of the sequence of partial sums $S\_n$ (where $S\_n$ represents the sum of the first $n$ terms of the sequence $\{a\_n\}$), i.e., $S = \lim_{n \to \infty} S\_n = \frac{a\_1}{1-q}$. Find the fractional form of the repeating decimal $0.\overline{72}$.

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