
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 $z=(2m^{2}+3m-2)+(m^{2}+m-2)i$ where $(m\in\mathbb{R})$, find the value of $m$ under the following conditions:  
$(1) z$ is a real number;  
$(2) z$ is an imaginary number;  
$(3) z$ is a pure imaginary number;  
$(4) z=0$.

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