
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
Given a cubic polynomial $ 60 x^3 - 80x^2 + 24x - 2 $, which has three roots $\alpha, \beta, \gamma$, all distinct and lying in the interval $(0, 1)$. Find the sum 
\[
\frac{1}{1-\alpha} + \frac{1}{1-\beta} + \frac{1}{1-\gamma}.
\]

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