
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 $U = \mathbb{R}$, $A = \{x | 0 \leq x \leq 3\}$, $B = \{x | m-1 \leq x \leq m+1\}$.  
$(1)$ If $m = 3$, find $A \cap (\complement_U B)$;  
$(2)$ If "$x \in B$" is a sufficient but not necessary condition for "$x \in A$", find the range of values for $m$.

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