
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 \(x^3 - 27x^2 + 98x - 72\). It is given that there exist real numbers \(A\), \(B\), and \(C\) such that 
\[
\frac{1}{s^3 - 27s^2 + 98s - 72} = \frac{A}{s-p} + \frac{B}{s-q} + \frac{C}{s-r}
\]
for all \(s \not\in \{p, q, r\}\). What is \(\tfrac{1}{A} + \tfrac{1}{B} + \tfrac{1}{C}\)?
A) 255
B) 256
C) 257
D) 258

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