
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 sets $A=\{x|-3\leqslant x\leqslant 5\}$, $B=\{x|m+1 < x < 2m-1\}$, and $C=\{x\in\mathbb{Z}|x\in A \text{ or } x\in B\}$.

$(1)$ When $m=3$, represent the set $C$ by listing its elements.

$(2)$ If $A\cap B=B$, find the range of the real number $m$.

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