
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 \(x^3 - 21x^2 + 130x - 210\). It is given that there exist real numbers \(A\), \(B\), and \(C\) such that 
\[
\dfrac{1}{s^3 - 21s^2 + 130s - 210} = \dfrac{A}{s-p} + \dfrac{B}{s-q} + \dfrac{C}{s-r}
\]
for all \(s \not\in \{p, q, r\}\). What is \(\tfrac1A + \tfrac1B + \tfrac1C\)?
A) 273
B) 274
C) 275
D) 276
E) 277

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