
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 set $A=\{x\left|\right.-2\leqslant x\leqslant 2\}$, set $B=\{x|\frac{x-5}{x}≤0\}$.<br/>$(1)$ Let $a$ be a real number. If set $C=\{x\left|\right.3a\leqslant x\leqslant 2a+1\}$, and $C\subseteq (A$⋂$B)$, find the range of $a$;<br/>$(2)$ Let $m$ be a real number. If set $D=\{x|m≤x≤m+\frac{1}{2}\}$, and "$x\in (A$⋃$B)$" is a necessary but not sufficient condition for "$x\in D$", determine if there exists a value of $m$ that satisfies the condition. If it exists, find the range of $m$; if not, explain the reason.

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