
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 $U = \mathbb{R}$, $A = \{x | 0 \leqslant x \leqslant 5\}$, $B = \{x | m-1 \leqslant x \leqslant 2m+1\}$.  
$(1)$ If $m = 3$, find $A$ ⋂ $(C_U B)$.  
$(2)$ If "$x \in B$" is a sufficient and necessary condition for "$x \in A$", find the range of real number $m$.

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