
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
Liu Hui was one of the most outstanding mathematicians in ancient China. His most significant contribution to the history of Chinese arithmetic was his annotation of "The Nine Chapters on the Mathematical Art". In the chapter on circle measurement, Liu Hui proposed the idea of "repeatedly dividing until it cannot be divided any further, and thus merging with the circle without any loss". This idea reflects the method of transforming the infinite into the finite, which has been widely applied. For instance, the formula $$2+ \frac {1}{2+ \frac {1}{2+\cdots }}$$ is a definite value x (the ellipsis in the formula indicates an infinite repetition according to this rule). The value of this formula can be obtained through the following method: Let the original formula equal x, then $$2+ \frac {1}{x}=x$$, which leads to x<sup>2</sup>\-2x-1=0. Solving this equation gives $$x=1± \sqrt {2}$$. Taking the positive value, we get $$x= \sqrt {2}+1$$. Using a similar method, find the value of $$\sqrt {6+ \sqrt {6+ \sqrt {6+…}}}$$.

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