
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}
user