
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
Let the function $f(x)= \sqrt {1-x^{2}}$, $g(x)=a(x+b)(0 < a\leqslant 1,b\leqslant 0)$.  
$(1)$ Discuss the parity of the function $y=f(x)\cdot g(x)$;  
$(2)$ When $b=0$, determine the monotonicity of the function $y= \frac {g(x)}{f^{2}(x)}$ on $(-1,1)$ and explain the reason;  
$(3)$ Let $h(x)=|af^{2}(x)- \frac {g(x)}{a}|$, if the maximum value of $h(x)$ is $2$, find the range of values for $a+b$.

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