
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 $U=\mathbb{R}$, $A=\{x|f(x)= \sqrt{(x-1)(x-2)}\}$, $B=\{x|\log_{2}(x-a) < 1\}$.  
(1) If $a=1$, find $(\complement_{U}A) \cap B$.  
(2) If $(\complement_{U}A) \cap B = \emptyset$, find the range of the real number $a$.

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