
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 $p$, $q$, $r$ be the roots of the cubic polynomial $x^3 - 2x - 2 = 0$. Find
\[
p(q - r)^2 + q(r - p)^2 + r(p - q)^2.
\]

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