
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 set $A=\{x|(x+2m)(x-m+4)<0\}$, where $m\in \mathbb{R}$, and the set $B=\left\{ x\left| \frac{1-x}{x+2} > 0 \right.\right\}$.

$(1)$ If $B\subseteq A$, find the range of the real number $m$;

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

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