
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
Find the value of the real number $m$ such that the complex number $z=2m^2-3m-2+(m^2-3m+2)i$ is respectively:  
(1) a real number;  
(2) a pure imaginary number;  
(3) zero.

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