
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 $A=\left(a-\frac{a^2}{a+b}\right)÷\frac{a^2b^2}{a^2-b^2}$.  
$(1)$ Simplify $A$.  
$(2)$ If point $P(a,b)$ is the intersection point of the line $y=x-3$ and the inverse proportion $y=\frac{2}{x}$, find the value of $A$.

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