
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
Given a complex number $z=\dfrac{m^{2}-m-6}{m+3}+\left(m^{2}-2m-15\right)i$ (where $i$ is the imaginary unit).

(1) If the complex number $z$ is a real number, find the value of the real number $m$.

(2) If the complex number $z$ is an imaginary number, find the range of values for the real number $m$.

(3) If the complex number $z$ is a purely imaginary number, find the value of the real number $m$.

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