
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
(1) Given sets $A=\{x|-8<x<-2\}$, and $B=\{x|x<-3\}$, find $A\cup B$ and $A\cap (\complement_{\mathbb{R}} B)$;  
(2) Let the function $f(x)=\sqrt{4-2^x}+\ln(x+1)$ have a domain of $C$, find $C$.

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