
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 that the solution set of the quadratic inequality $x^{2}-3x+2 \gt 0$ is $A$, and the solution set of the inequality $mx^{2}-(m+2)x+2 \lt 0$ with respect to $x$ is $B$ (where $m\in R$).  
$(Ⅰ)$ Find the set $B$;  
$(Ⅱ)$ Choose one of the following conditions: $B\subseteq \complement _{R}A$, $A\cap B\neq \varnothing$, or $A\cup B=A$, and complete the blank in the question below. If there exists a real number $m$, find the range of $m$; if not, explain the reason.  
Question: Is there a real number $m$ such that _____? (Note: If multiple conditions are chosen and answered separately, the first answer will be scored).

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