
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 universe $U=\{x \mid x\geq -4\}$, set $A=\{x \mid -1<x\leq 3\}$, and set $B=\{x \mid 0\leq x<5\}$, find $A\cap B$, $(\complement_U A)\cup B$, and $A\cap (\complement_U B)$.

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