
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 $U=\{x|x\leq5\}$, set $A=\{x|-2<x<3\}$, and set $B=\{x|-4<x\leq2\}$.  
Find: $A\cap B$, $A\cap C_{U}B$, $(C_{U}A)\cup B$, and $(C_{U}A)\cup (C_{U}B)$.

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