
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
For an infinite geometric sequence $\{a_n\}$ with a common ratio $|q| < 1$ (i.e., the sequence has an infinite number of terms), we define $\lim_{n\rightarrow \infty} S_n$ (where $S_n$ is the sum of the first $n$ terms of the sequence $\{a_n\}$) as the sum of its terms, denoted by $S$, i.e., $S= \lim_{n\rightarrow \infty} S_n = \frac{a_1}{1-q}$. Then, the fractional form of the repeating decimal $0.\overline{72}$ is \_\_\_\_\_\_.

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