
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 $f(x)= \sqrt {3+2x-x^{2}}$ has a domain of $A$, and the set $B=\{x|x^{2}-2mx+m^{2}-9\leqslant 0\}$.  
$(1)$ If $A\cap B=[2,3]$, find the value of the real number $m$;  
$(2)$ If for every $x_{1} \in A$, there exists $x_{2} \in (\mathbb{C}_R B)$ such that $x_{2}=x_{1}$, find the range of the real number $m$.

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