
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 $A=\{x|x\in[-2,5]\}$, $B=\{x|x^{2}-3mx+2m^{2}-m-1 \lt 0\}$.<br/>$(1)$ When $x\in \mathbb{N}$, find the number of non-empty proper subsets of $A$;<br/>$(2)$ If $A\cap B=B$, find the range of real number $m$.

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