
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 sets $A=\{x \mid -2<x<4\}$ and $B=\{x \mid x-m<0\}$:  
(1) If $m=3$ and the universal set $U = A \cup B$, find $A \cap \complement_U B$;  
(2) If $A \cap B = \emptyset$, determine the set of real numbers for $m$;  
(3) If $A \cap B = A$, determine the set of real numbers for $m$.

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