
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 $ax^2 - 3x + 6 > 4$ has the solution set $\{x|x < 1 \text{ or } x > b\}$.  
   (1) Find the values of the real numbers $a$ and $b$;  
   (2) When $c > 2$, solve the inequality $ax^2 - (ac + b)x + bc < 0$.

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