
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 a complex number $z=(m^{2}-m)+(m-1)i$ where $m\in \mathbb{R}$.<br/>$(Ⅰ)$ If $z$ is a real number, find the value of $m$;<br/>$(Ⅱ)$ If $z$ is a purely imaginary number, find the value of $m$;<br/>$(Ⅲ)$ If the complex number $z$ corresponds to a point in the first quadrant, find the range of values for $m$.

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