
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 $A=\{x|-1\leqslant x\leqslant 4\}$, $B=\{x|m-1 < x < 3m+1\}$,

$(1)$ When $x\in\mathbb{N}^{*}$, find the number of subsets of $A$;  
$(2)$ When $x\in\mathbb{R}$ and $A\cap B=B$, find the range of $m$.

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