
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 set $A=\{x|x^{2}+3x-28 \lt 0\}$, set $B=\{x\left|\right.m-2 \lt x \lt m+1\}$.  
$(1)$ Given $p:3\in B$, if $p$ is a true proposition, find the range of real number $m$;  
$(2)$ If "$x\in A$" is a necessary but not sufficient condition for "$x\in B$", find the range of real number $m$.

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