
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 polynomial $40x^3 - 70x^2 + 32x - 3$. If the roots of this polynomial are $a$, $b$, and $c$, which are distinct real numbers strictly between $0$ and $1$, find 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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