
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 $ax^2-3x+2>0$, its solution set is $\{x|x<1 \text{ or } x>b\}$  
(1) Find the values of $a$ and $b$.  
(2) Solve the inequality $ax^2-(am+b)x+bm<0$.

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