
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 the complex number $z = (2m^2 - 3m - 2) + (m^2 - 3m + 2)i$.
- (I) For what value(s) of the real number $m$ is the complex number $z$ purely imaginary?
- (II) Simplify $\frac{z^2}{z + 5 + 2i}$ when $m = 0$.

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