
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 \(x^3 + 2x^2 + 4x + 6 = 0.\) Given that \(Q(x)\) is a cubic polynomial such that \(Q(a) = b + c\), \(Q(b) = a + c\), \(Q(c) = a + b\), and \(Q(a + b + c) = -10\), find \(Q(x).\)

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