
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 $z = (m^2 - 9m - 36) + (m^2 - 2m - 15)i$  
(1) a real number?  
(2) a complex number?  
(3) a pure imaginary number?

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