
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 the set $A=\{x|x^{2}-2x-8 < 0\}$, $B=\{x|x-m < 0\}$.  
$(1)$ If $m=3$, find $A\cap(\complement_{\mathbb{R}}B)$;  
$(2)$ If $A\cap B=\varnothing$, find the range of the real number $m$;  
$(3)$ If $A\cap B=A$, find the range of the real number $m$.

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