
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
For the inequality $a x^{2} + b x + c < 0$ where the solution set is $(-\infty, \alpha) \cup (\beta, +\infty)$ with $\alpha < \beta < 0$, find the solution set for the inequality $c x^{2} - b x + a > 0$.

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