
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 distinct roots of the polynomial \( x^3 - 30x^2 + 105x - 114 \). It is given that there exist real numbers \( A, B, \) and \( C \) such that for all \( s \) not in \( \{p, q, r\} \),
\[
\frac{1}{s^3 - 30s^2 + 105s - 114} = \frac{A}{s-p} + \frac{B}{s-q} + \frac{C}{s-r}
\]
What is \( \frac{1}{A} + \frac{1}{B} + \frac{1}{C} \)?
A) 295
B) 298
C) 300
D) 302

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