
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 \( x^3 - 15x^2 + 50x - 56 \). It is given that there exist real numbers \( A, B, \) and \( C \) such that 
\[
\frac{1}{s^3 - 15s^2 + 50s - 56} = \frac{A}{s-p} + \frac{B}{s-q} + \frac{C}{s-r}
\]
for all \( s \not\in \{p,q,r\} \). What is \( \frac{1}{A} + \frac{1}{B} + \frac{1}{C} \)?
A) 220
B) 222
C) 225
D) 227
E) 230

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