
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 $1+ \frac{1}{1+ \frac{1}{1+…}}$ ("…" indicates infinite repetition) is a fixed value, which allows us to set the original expression equal to $t$. By solving $1+ \frac{1}{t}=t$, we find its value to be $t= \frac{\sqrt{5}+1}{2}$. Using a similar method, we can find that $\sqrt{2+ \sqrt{2+ \sqrt{2+…}}}$ equals ______.

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