
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
Determine the values of $a$ and $b$ such that the solution set of the inequality $ax^2+bx-1 > 0$ is $\{x | 1 < x < 2\}$.  
(1) Determine the values of $a$ and $b$;  
(2) Find the solution set of the inequality $\frac{ax+1}{bx-1} > 0$.

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