
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 $z = (m^2 + 5m + 6) + (m^2 - 2m - 15)i$  
(1) equal the complex number $2 - 12i$;  
(2) become the conjugate of the complex number $12 + 16i$;  
(3) correspond to a point above the x-axis.

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