
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 $C={x|x < 2a+1}$, $B∩C=C$, find the range of the real number $a$.

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