
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
Let the set of real numbers be the universal set, $A=\left\{{x|{\frac{{x-3}}{{2x-1}}≤0}}\right\}$, $B=\{x|x^{2}-a \lt 0\}$.<br/>$(Ⅰ)$ When $a=4$, find $A\cap B$ and $A\cup B$;<br/>$(Ⅱ)$ If $B\cap (\complement _{R}A)=B$, find the range of real number $a$.

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