
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 \( x^3 + 4x^2 + 6x + 9 = 0 \). Given that \( P(x) \) is a cubic polynomial such that \( P(a) = b + c \), \( P(b) = a + c \), \( P(c) = a + b \), and \( P(a + b + c) = -20 \), find \( P(x) \).

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