
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 universal set $U = \mathbb{R}$, set $A = \{x | -2 \leq x \leq 4\}$, $B = \{x | m + 1 < x < 2m\}$.  
$(1)$ If $m = 3$, find $A \cup B$ and $A \cap B$;  
$(2)$ If $A \cap B = \emptyset$, find the range of real numbers for $m$.

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