
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 sets $A=\{x|y= \sqrt{x-1} + \sqrt{2-x}\}$, $B=\{y|y=2^{x}, x\geq a\}$  
(Ⅰ) If $a=2$, find $(\complement_{U}A) \cap B$;  
(Ⅱ) If $(\complement_{U}A) \cup B=\mathbb{R}$, find the range of the real number $a$.

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