
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 $ax^{2}-3x+2 > 0$ has the solution set $\{x|x < 1$ or $x > b\}$  
$(1)$ Find the values of $a$ and $b$;  
$(2)$ Solve the inequality with respect to $x$: $x^{2}-b(a+c)x+4c > 0$.

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