
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
Find the value of \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}\) for real numbers \(A\), \(B\), and \(C\) where:
\[
\frac{1}{s^3 - 24s^2 + 143s - 210} = \frac{A}{s-p} + \frac{B}{s-q} + \frac{C}{s-r}
\]
and \(p\), \(q\), and \(r\) are the roots of the polynomial \(x^3 - 24x^2 + 143x - 210\).
A) 242
B) 243
C) 245
D) 246

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