
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 $A=\left\{{x∈N|{\frac{1}{3}＜x＜4}}\right\}$ and $B=\{x\left|\right.2x-a\geqslant 0\}$.<br/>$(1)$ When $a=5$, find $A\cap B$;<br/>$(2)$ If $(\complement _{R}B)\cap A=\varnothing $, find the range of real number $a$.

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