
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 $ax^{2}+3x+2 \gt 0$ where $a\in R$.  
$(1)$ If the solution set of $ax^{2}+3x+2 \gt 0$ is $\{x|b \lt x \lt 1\}$, find the values of the real numbers $a$ and $b$.  
$(2)$ Find the solution set of the inequality $ax^{2}-3x+2 \gt ax-1$.

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