
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 $p$, $q$, and $r$ be the distinct roots of the polynomial $x^3 - 24x^2 + 98x - 75$. It is given that there exist real numbers $A$, $B$, and $C$ such that \[\dfrac{5}{s^3 - 24s^2 + 98s - 75} = \dfrac{A}{s-p} + \dfrac{B}{s-q} + \frac{C}{s-r}\]for all $s\not\in\{p,q,r\}$. What is $\tfrac1A+\tfrac1B+\tfrac1C$?
A) 253
B) 254
C) 255
D) 256
E) 257

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