
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 $U=\mathbb{R}$, and the set $A=\{x|x^2-x-6<0\}$, $B=\{x||x|=y+2, y\in A\}$. Find $C_{U}B$, $A\cap B$, $A\cup B$, $A\cup (C_{U}B)$, $A\cap (B)$, $C_{U}(A\cup B)$, $(C_{U}A)\cap (C_{U}B)$.

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