
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 $ax^{2}-3x+2 < 0$ with the solution set $A=\{x\mid1 < x < b\}$.

(1) Find the values of $a$ and $b$;
(2) Find the minimum value of the function $f(x)=(2a+b)x-\frac{1}{(a-b)(x-1)}$ $(x\in A)$.

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