
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 \( p, q, r, s \) be the roots of the quartic polynomial \(x^4 - x^2 - x - 2 = 0\). Find the value of:
\[ p(q-r)^2 + q(r-s)^2 + r(s-p)^2 + s(p-q)^2. \]

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