
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
For what value of the real number $m$ is $Z = (m^2 - 2m - 3) + (m^2 + 3m + 2)i$
(1) purely imaginary;
(2) real;
(3) corresponds to a point in the second quadrant of the complex plane.

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