
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
The solution set of the inequality $ax^2 + 5x - 2 > 0$ is $\left\{x|\frac{1}{2} < x < 2\right\}$. Determine the solution set of the inequality $ax^2 - 5x + a^2 - 1 > 0$.

A) $\left\{x|-3 < x < \frac{1}{2}\right\}$
B) $\left\{x|-2 < x < \frac{1}{3}\right\}$
C) $\left\{x|x < -3 \text{ or } x > \frac{1}{2}\right\}$
D) $\left\{x|x < -2 \text{ or } x > \frac{1}{3}\right\}$

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