
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
Let the complex number $z = (m^2 - 3m + 2) + (2m^2 - 5m + 2)i$ where $m \in \mathbb{R}$,

(Ⅰ) If $z$ is a real number, find the value of $m$;  
(Ⅱ) If the point corresponding to $z$ is located in the fourth quadrant of the complex plane, find the range of $m$.

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