
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 the quadratic equation with real coefficients \( x^{2} + ax + 2b - 2 = 0 \), the equation has two distinct real roots, one of which is in the interval \( (0, 1) \) and the other in the interval \( (1, 2) \). Determine the range of values for \( \frac{b-4}{a-1} \).

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