
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 $U=\mathbb{R}$, the domain of the function $f(x)= \frac{1}{\sqrt{x+2}}+\log(3-x)$ is the set $A$, and the set $B=\{x\mid x^2-a<0\}$  
(1) Find the complement of $A$ in $U$;  
(2) If $A \cup B = A$, find the range of the real number $a$.

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