
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 $U=\mathbb{R}$, $A=\{x|-4\leq x<2\}$, $B=\{x|-1<x\leq 3\}$, $P=\{x|x\leq 0 \text{ or } x\geq \frac{5}{2}\}$, find $A\cap B$, $(\complement_{U}B)\cup P$, and $(A\cap B)\cap (\complement_{U}P)$.

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