
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
Define $s_k$ as the sum of the $k^{th}$ powers of the roots of the polynomial $x^4 - 6x^3 + 11x^2 - 6x + 9 = 0$. Let $s_0=4$, $s_1=6$, and $s_2=14$. Let $a$, $b$, $c$ be real numbers such that for $k \geq 3$, $s_{k+1} = a s_k + b s_{k-1} + c s_{k-2}$. Determine the value of $a+b+c$.
A) -25
B) -19.67
C) -20
D) 0

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