
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 $ax^2 - 3x + 2 < 0$ is $A=\{x|1<x<b\}$,
(1) Find the values of $a$ and $b$;
(2) Find the minimum value of the function $f(x) = (2a+b)x - \frac{9}{(a-b)x}$ for $x \in A$.

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