
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 \( 40x^3 - 60x^2 + 28x - 2 \). If its roots are \( a, b, c \), all distinct and lying 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}
user