
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 $A=\{x | -3 \lt x \lt 6\}$, $B=\{x | a-2 \leqslant x \leqslant 2a-3\}$.  
$(1)$ When $a=5$, find $(\complement _{U}A)\cup B$;  
$(2)$ If $A\cup B=A$, find the range of values for $a$.

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