
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 the cubic equation \(40x^3 - 60x^2 + 25x - 1 = 0\) with roots \(a, b, c\). All roots are distinct real numbers strictly between 0 and 1. Calculate 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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