
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 the set $U=\{x|x>0\}$, $A=\{x|2\leq x<4\}$, $B=\{x|3x-7\geq 8-2x\}$.  
Find:  
(1) $A\cap B$, $A\cup B$, $C_U(A\cup B)$, $(C_UA)\cap B$;  
(2) If the set $C=\{x|2x+a>0\}$, and it satisfies $B\cup C=C$, find the range of the real number $a$.

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