
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
Let $m \in \mathbb{R}$, and the complex number $Z = (2+i)m^2 - 3(1+i)m - 2(1-i)$. For what value(s) of the real number $m$ is the complex number $Z$:
(1) a real number;
(2) a pure imaginary number;
(3) a complex number corresponding to a point on the bisector of the first and third quadrants in the complex plane.

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