
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 $U=\mathbb{R}$, set $A=\{x|1\leq x \leq 4\}$, $B=\{x|a\leq x \leq a+2\}$.  
(Ⅰ) If $a=3$, find $A\cup B$, $B\cap (\complement_{U}A)$;  
(Ⅱ) If $B\subseteq A$, find the range of $a$.

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