
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 $A=\{x|-1<x<5\}$, $B=\{x|2<x<8\}$.  
(1) Find $A\cap (\complement_{U}B)$ and $(\complement_{U}A) \cap (\complement_{U}B)$;  
(2) If set $C=\{x|a+1\leq x\leq 2a-2\}$, and $(\complement_{U}A) \cap C=\{x|6\leq x\leq b\}$, find the value of $a+b$.

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