
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
Consider the polynomial $x^3 - 7x^2 + 12x - 18$. Let $s_k$ be the sum of the $k$th powers of its roots. Given $s_0 = 3$, $s_1 = 7$, $s_2 = 13$, find the value of $a + b + c$ if the recursive relationship $s_{k+1} = a \cdot s_k + b \cdot s_{k-1} + c \cdot s_{k-2}$ holds for $k = 2, 3, \dots$.
A) -6
B) -3 
C) 0 
D) 3 
E) 6

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