
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 \( p, q, r \) be the three distinct real roots of the polynomial \( x^3 - 22x^2 + 80x - 67 \). Given the partial fraction decomposition of the rational function 
\[
\frac{1}{s^3 - 22s^2 + 80s - 67} = \frac{A}{s-p} + \frac{B}{s-q} + \frac{C}{s-r},
\]
find \(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\).

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