
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
\[ 
x^3 + 3x^2 + 5x + 7 = 0 
\]
The cubic polynomial \( P \) satisfies the following conditions:
\[ 
\begin{array}{l}
P(a) = b + c, \quad P(b) = a + c, \\
P(c) = a + b, \quad P(a + b + c) = -16.
\end{array}
\]
Determine the value of \( P(0) \).

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