
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 $U$ as $\mathbb{R}$, set $A=\{x|2\leq x<4\}$, $B=\{x|3x-7\geq8-2x\}$, and $C=\{x|x<a\}$.  
(1) Find $A\cap B$;  
(2) Find $A\cup (\complement_{U} B)$;  
(3) If $A\subseteq C$, find the range of $a$.

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