
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 $s_k$ denote the sum of the $k$th powers of the roots of the polynomial $x^3 - 6x^2 + 11x - 6$. Given $s_0=3$, $s_1=6$, and $s_2=14$, and let $a$, $b$, and $c$ be real numbers such that $s_{k+1} = a \, s_k + b \, s_{k-1} + c \, s_{k-2}$ for $k = 2$, $3$, .... What is $a+b+c$?
A) 12
B) 13
C) 14
D) 15
E) 16

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