
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 $A={ x| 1{ < }x{ < }b },$ find the values of $a$ and $b$. Then, find the minimum value of the function $f(x){=}(2a{+}b)x{-}\frac{9}{(a{-}b)x}$ where $x\in A$.

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