
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
Let \( a, b, c \) be the roots of \( x^3 - 9x^2 + 11x - 1 = 0 \), and let \( s = \sqrt{a} + \sqrt{b} + \sqrt{c} \). Find \( s^4 - 18s^2 - 8s \).

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