
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 $x^3 - 2x^2 + 3x + 4 = 0.$ Given that $Q(x)$ is a cubic polynomial such that $Q(p) = q + r,$ $Q(q) = p + r,$ $Q(r) = p + q,$ and $Q(p + q + r) = -20,$ find $Q(x).$

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