
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 that the solution set of the inequality $ax^{2}-3x+b \gt 4$ is $\{x\left|\right.x \lt 1$ or $x \gt 2\}$.  
$(1)$ Find the values of $a$ and $b$;  
$(2)$ Solve the inequality $ax^{2}-\left(ac+2\right)x+2c \lt 0$.

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