
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 $U=\mathbb{R}$, $A=\{x|x^2-4>0\}$, $B=\{x|x\leq a\}$;  
(1) If $a=1$, find $A\cap B$, $A\cup B$;  
(2) If $\complement_{U}A \subseteq B$, find the range of the real number $a$.

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