
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 ancient Chinese mathematical classic "The Nine Chapters on the Mathematical Art," there is a passage about the method of exhausting a circle: "When you divide it as thinly as possible, what is lost is negligible. By dividing it again and again until it cannot be divided any further, it merges with the circumference of the circle and there is no loss." This reflects a process of transforming the infinite into the finite. For example, in $\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}$, the "..." represents an infinite repetition, but the original expression is a definite value $x$. This can be determined by the equation $\sqrt{2+x}=x$, which gives $x=2$. By analogy with the aforementioned method, find the value of $1+\frac{1}{1+\frac{1}{1+\cdots }}$.

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