
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
In the "Circular Field Method" of the "Chapter on the Method of Field Allocation" in "The Nine Chapters on the Mathematical Art" (annotated by Liu Hui), it is stated that: "The more you divide, the less you lose. Divide again and again until it cannot be divided, then it will merge with the circumference and there will be no loss." The division method used in the annotation is a process of transforming the infinite into the finite. For example, in $\sqrt{2+\sqrt{2+\sqrt{2+\ldots}}}$, "$\ldots$" represents infinite repetition, but the original expression is a definite value $x$, which can be determined by the equation $\sqrt{2+x}=x$ to be $x=2$. Similarly, it is not difficult to obtain $\frac{1}{1+\frac{1}{1+\ldots}}=$ _______.

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