
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 expression $1+\dfrac{1}{1+ \dfrac{1}{1+t}}$ where the ellipsis "..." indicates infinite repetition, since the original expression is a fixed value, it can be obtained by the following method: Let the original expression $=t$, then $1+\dfrac{1}{t} =t$, thus $t^{2}-t-1=0$, taking the positive value gives $t=\dfrac{ \sqrt{5}+1}{2}$. By a similar method, we can obtain $\sqrt{2+ \sqrt{2+ \sqrt{2+…}}} = \_\_\_\_\_\_$.

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