
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 $z = (1-m^2) + (m^2-3m+2)i$, where $m \in \mathbb{R}$,

(I) If the complex number $z = 0$, find the value of $m$;

(II) If the complex number $z$ is purely imaginary, find the value of $m$;

(III) If the point represented by the complex number $z$ in the complex plane is in the third quadrant, find the range of values for $m$.

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