
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 $A=\{x|y=\lg (-x^{2}+5x-4)\}$ and $B=\{x|x^{2}-\left(a+2\right)x+2a\leqslant 0\}$.<br/>$(1)$ When $a=3$, find $A\cup \complement _{R}B$;<br/>$(2)$ If "$x\in A$" is a necessary but not sufficient condition for "$x\in B$", find the range of real number $a$.

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