
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 $U=\mathbb{R}$, set $A=\{x|x>4\}$, and set $B=\{x|-6<x<6\}$.  
(1) Find $A\cap B$ and $A\cup B$;  
(2) Find the complement of $B$ in $U$, denoted as $\complement_U B$;  
(3) Define $A-B=\{x|x\in A, \text{ and } x\notin B\}$, find $A-B$ and $A-(A-B)$.

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