
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 \( x^3 - 20x^2 + 99x - 154 \). It is given that there exist real numbers \( A \), \( B \), and \( C \) such that 
\[
\dfrac{1}{t^3 - 20t^2 + 99t - 154} = \dfrac{A}{t-p} + \dfrac{B}{t-q} + \dfrac{C}{t-r}
\]
for all \( t \not\in \{p,q,r\} \). Find the value of \( \frac1A + \frac1B + \frac1C \).
A) 199
B) 227
C) 220
D) 245

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