
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
Consider another cubic equation $20x^3 - 34x^2 + 15x - 1 = 0$. Assume its roots, $a, b,$ and $c$, are distinct and lie strictly between $0$ and $1$. Compute the sum:
\[ \frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c} \]

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