
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 the function $f(x)=\sqrt{1+x}+\sqrt{1-x}$.  
$(1)$ Find the domain and range of $f(x)$;  
$(2)$ Let $h(x)=\frac{{f(x)}}{{2\sqrt{1-{x^2}}+6}}$. If the inequality $h(x)≤\frac{3}{4}{m^2}-\frac{1}{2}am$ holds for any $x\in \left[-1,1\right]$ and any $a\in \left[-1,1\right]$, find the range of the real number $m$.

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