
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 $U=\mathbb{R}$. If set $A=\{x|3\leq x<8\}$, and $B=\{x|2<x\leq6\}$, then  
(1) Find $A\cap B$, $A\cup B$, $\complement_U A$;  
(2) If set $C=\{x|x\geq a\}$, and $A\subseteq C$, find the range of $a$.

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