
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
Let the universal set be $U = \mathbb{R}$, set $A = \{x | -4 \leq x < 2\}$, $B = \{x | -1 < x \leq 3\}$, $P = \{x | x \leq 0$ or $x \geq \frac{5}{2}\}$. Find:<br/>
$(1) A \cap B$;<br/>
$(2) (\complement_{U}B) \cup P$.

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