
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 the cubic polynomial $x^3 - 3x - 2 = 0.$  Find
\[
a^2(b - c)^2 + b^2(c - a)^2 + c^2(a - b)^2.
\]

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