
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 sets $A=\{x| -4 \leqslant x \leqslant -2\}$, $B=\{x| x+3 \geqslant 0\}$, and $U=\{x| x \leqslant -1\}$.  
$(1)$ Find $A$ ⋂ $B$ and $A$ ⋃ $B$.  
$(2)$ Find $\complement _{U}(A \cap B)$.

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