
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 set $U=\{x|1\leqslant x\leqslant 7\}$, $A=\{x|2\leqslant x \lt 5\}$, $B=\{x|3 \lt x\leqslant 7\}$.  
$(1)$ Find $A\cap B$;  
$(2)$ Find $(\complement _{U}A)\cup B$.

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