
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
Definition: For an infinite geometric series $\{a_{n}\}$ with a common ratio $q\left(0 \lt |q| \lt 1\right)$, the sum of all terms is $\frac{{a}_{1}}{1-q}$. That is, as $n$ approaches infinity, ${S}_{n}=\frac{{a}_{1}(1-{q}^{n})}{1-q}$ approaches $\frac{{a}_{1}}{1-q}$. By using this definition, infinite recurring decimals can be converted into fractional form $\frac{a}{b}$ where $a$ and $b$ are integers, $b\neq 0$, and $a$ and $b$ are coprime. Therefore, the fractional form of $5.\dot{2}\dot{5}$ is ______.

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