
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 $U=\mathbb{R}$, let set $A=\{x|0<\log_{2}x<2\}$, and $B=\{x|x\leq3m-4 \text{ or } x\geq8+m\}$ ($m<6$).  
(1) If $m=2$, find $A\cap(\complement_{U}B)$;  
(2) If $A\cap(\complement_{U}B)=\emptyset$, find the range of the real number $m$.

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