
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 $ax^{2}-3x+2 \gt 0$ is $\left\{x\left|\right.x \lt 1 \text{ or } x \gt b\right\}$.

(1) Find the values of real numbers $a$ and $b$.

(2) Solve the inequality $ax^{2}-\left(ac+b\right)x+bc\leqslant 0 \left(c\in \mathbb{R}\right)$.

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