
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
What values should the real number $x$ take so that the complex number $z = (x^2-2x-3) + (x^2+3x+2)i$ (where $i$ is the imaginary unit) is:
(1) a real number?
(2) represented by a point in the second quadrant of the complex plane?

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