
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
Given $s_k$ denote the sum of the kth powers of the roots of the polynomial $x^3-5x^2+8x-13$, where $s_0=3$, $s_1=5$, and $s_2=9$, and for $k=2,3,...$, $s_{k+1} = a \, s_k + b \, s_{k-1} + c \, s_{k-2}$, calculate $a+b+c$.

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