
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 square roots of a positive real number $x$ are $a$ and $a+b$.  
$(1)$ If $a=-2$, find the values of $b$ and $x$;  
$(2)$ If $b=6$, find the values of $a$ and $x$;  
$(3)$ If $a^{2}x+\left(a+b\right)^{2}x=8$, find the value of $x$.

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