
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 \(x^3 - 8x^2 + 17x - 14\) whose roots are denoted as \( p, q, \) and \( r \). Let \( s_k \) denote the sum of the \( k \)th powers of these roots. Given \( s_0=3 \), \( s_1=8 \), and \( s_2=17 \), suppose there exists a relation \( s_{k+1} = a s_k + b s_{k-1} + c s_{k-2} \) for \( k=1, 2, 3, \ldots \). Determine the sum \( a+b+c \).
A) \(6\)
B) \(7\)
C) \(8\)
D) \(9\)

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