
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 sets $A=\{x\left|\right.-3\leqslant x \lt 4\}$ and $B=\{x\left|\right.2m-1\leqslant x\leqslant m+1\}$.<br/>$(1)$ If $B\subseteq A$, find the range of real number $m$;<br/>$(2)$ Proposition $q$: "$\exists x\in A$, such that $x\in B$" is a true proposition, find the range of real number $m$.

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