
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 equation $x^3 - 6x^2 + 11x - 6 = 0$. Given that $Q(x)$ is a cubic polynomial such that $Q(a) = b + c$, $Q(b) = a + c$, $Q(c) = a + b$, and $Q(a + b + c) = -27$, find $Q(x)$.

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