
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 algebraic expression $1+ \frac{1}{1+ \frac{1}{1+\cdots}}$ contains an ellipsis "$\cdots$" that represents an infinite repetition of this pattern. Since the original expression is a fixed value, it can be calculated using the following method: let the original expression $=t$, then $1+\frac{1}{t}=t$, which leads to ${{t}^{2}}-t-1=0$. By taking the positive value, we get $t=\frac{\sqrt{5}+1}{2}$. A similar method can be used to find $\sqrt{6+ \sqrt{6+ \sqrt{6+\cdots}}}$ _____.

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