
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
Consider the infinite continued fraction:
$$
1 + \frac {1}{1 + \frac {1}{1 + \cdots}}
$$
where ellipsis ("…") indicates the pattern continues indefinitely. Since the original expression has a fixed value, we can solve for it as follows: Let the original expression equal $t$. Then, we have $1 + \frac {1}{t} = t$. Solving the quadratic equation $t^2 - t - 1 = 0$ and taking the positive value, we get $t = \frac {\sqrt {5} + 1}{2}$. Similarly, find the value of:
$$
\sqrt {6 + \sqrt {6 + \sqrt {6 +\cdots}}}
$$

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