
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: $A=\frac{2}{{{a^2}-4}}-\frac{1}{{a({a-2})}$.  
$(1)$ Simplify $A$;  
$(2)$ Choose one of the following two conditions as known, and find the value of $A$.  
Condition 1: If point $P(a,a+2)$ lies on the graph of the inverse proportion function $y=\frac{8}{x}$;  
Condition 2: If $a$ is a root of the equation $x^{2}+x=8-x$.

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