
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 the set $A=\{x|\frac{x-a}{x-3a}＜0\}(a≠0)$, the solution set of the inequality $x^{2}-5x+6 \lt 0$ is denoted as $B$.<br/>$(1)$ When $a=1$, find $A\cup B$;<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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