
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 $1 + \frac{1}{1 + \frac{1}{1 + \cdots}}$ where the ellipsis "..." indicates the pattern repeats indefinitely, represents a fixed value that can be determined as follows: Let the original expression be $t$, then we have $1 + \frac{1}{t} = t$, which leads to $t^2 - t - 1 = 0$. Taking the positive value, we get $t = \frac{\sqrt{5} + 1}{2}$. Similarly, the value of $\sqrt{6 + \sqrt{6 + \sqrt{6 + \ldots}}} =$ ______ .

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