
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 sets $A=\{x|4\leq x<8, x\in \mathbb{R}\}$, $B=\{x|6<x<9, x\in \mathbb{R}\}$, $C=\{x|x>a, x\in \mathbb{R}\}$.  
(1) Find $A\cup B$;  
(2) $(\complement_{U}A) \cap B$;  
(3) If $A\cap C=\emptyset$, find the range of $a$.

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