
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 values of the real number $m$ does the complex number $z=m^{2}\left( \frac{1}{m+5}+i\right)+(8m+15)i+\frac{m-6}{m+5}$

(1) become a real number;

(2) become a complex number;

(3) become a purely imaginary number;

(4) correspond to a point in the second quadrant.

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