
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(s) of the real number $m$ does $z= \dfrac {m^{2}-m-6}{m+3}+(m^{2}+5m+6)\cdot i$  
$(1)$ become a real number;  
$(2)$ become an imaginary number;  
$(3)$ become a pure imaginary number;  
$(4)$ make the point corresponding to the complex number $z$ lie in the second quadrant of the complex plane.

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