
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
(The full score of this question is 12 points)  
It is known that the solution set of the inequality $ax^2-3x+6>4$ is $\{x|x<1 \text{ or } x>b\}$,  
(1) Find $a$, $b$;  
(2) Solve the inequality $ax^2-(ac+b)x+bc<0$.

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