
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 function $$f(x)= \sqrt {6-2x}+\lg(x+2)$$, its domain is set A, and B={x|x>3 or x<2}.  
(1) Find A∩B;  
(2) If C={x|x<2a+1}, and B∩C=C, find the range of the real number a.

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