
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 that \(0 < \alpha < \beta\) and the solution set of the quadratic inequality \(a x^{2}+b x+c>0\) is \(\{x \mid \alpha < x < \beta\}\), determine the solution set of the inequality
$$
(a + c - b) x^{2} + (b - 2a) x + a > 0.
$$

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