
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 real number $m$ is the complex number $$z= \frac {m^{2}-m-6}{m+3}+(m^{2}-2m-15)i$$  
(1) a real number?  
(2) a complex number?  
(3) a purely imaginary number?

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