
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
The conversion between finite and infinite is an important idea in mathematics. For instance, in the "Circle Field Method" from the "Nine Chapters on the Mathematical Art" (annotated by Liu Hui), it is stated: "Divide and divide again until it cannot be divided, then it will merge with the circle and nothing will be lost." This illustrates that the "Circle Division Method" is a process of converting between the infinite and the finite. Similarly, in the expression $\sqrt{2+\sqrt{2+\sqrt{2+\ldots }}}$, "..." represents an infinite repetition, but the original expression is a definite value $x$, which can be determined through the equation $\sqrt{2+x}=x$ to be $x=2$. Likewise, a repeating decimal can be converted into a fraction. What is the fractional representation of $0.36$?

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