
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 $a$, $b$, and $c$ be the distinct roots of the polynomial $x^3 - 18x^2 + 91x - 170$. It is given that there exist real numbers $D$, $E$, and $F$ such that \[\dfrac{1}{s^3 - 18s^2 + 91s - 170} = \dfrac{D}{s-a} + \dfrac{E}{s-b} + \dfrac{F}{s-c}\] for all $s\not\in\{ a,b,c \}$. What is $D+E+F$?
A) -1
B) 0
C) 1
D) 2

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