
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 $A=\{x|x^2+4x>0\}$, $B=\{x|a-1<x<a+1\}$, where $x\in \mathbb{R}$, and let $U=\mathbb{R}$.  
(1) Find the complement of $A$ in $U$, $\complement_U A$;  
(2) If $B \subseteq \complement_U A$, find the range of real number $a$.

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