
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 $m$ is a real number, $A=\{x|x^{2}-(m+1)x+m=0\}$, $B=\{x|x\cdot m-1=0\}$.  
$(1)$ When $A\subseteq B$, find the set of possible values for $m$;  
$(2)$ When $B$⫋$A$, find the set of possible values for $m$.

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