
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 domain of the function $y=\sqrt{4-{x}^{2}}$ is $A$, the solution set of $x^{2}+6x+8 \gt 0$ is $B$, $C=\{x\in R\left|\right.3-2m\leqslant x\leqslant 2+m,m\in R\}$, and the range of the function $y=\frac{6x-17}{3-x}(x \gt 2)$ is $D$.<br/>$(Ⅰ)$ If "$x\in A$⋂$B$" is a sufficient condition for "$x\in C$", find the range of $m$;<br/>$(Ⅱ)$ If $B$⋃$C=R$, and $C\subseteq D$, find the range of $m$.

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