
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 in terms of _\(x\)_, \(ax^2+bx+c < 0\)'s solution set is \(\left\{x\left|x < -2 \text{ or } x > - \frac{1}{2} \right.\right\}\), then the solution set for the inequality in terms of _\(x\)_, \(ax^2-bx+c > 0\) is ______.

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