
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 $z = (m^2 - 1) + (m^2 - 3m + 2)i$, where $m \in \mathbb{R}$:  
(1) If the complex number $z = 0$, find the value of $m$;  
(2) If the complex number $z$ is purely imaginary, find the value of $m$;  
(3) If the point represented by the complex number $z$ in the complex plane is in the second quadrant, find the range of values for $m$.

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