
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 inequality $ax^{2} + 5x - 2 > 0$ has the solution set $\{x|\frac{1}{2} < x < 2\}$,  
(1) Find the value of the real number $a$;  
(2) Find the solution set of the inequality $ax^{2} - 5x + a^{2} - 1 > 0$.

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