
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 $m$ is the complex number $z=m^2-1+(m^2-m-2)i$ respectively:  
(1) a real number?  
(2) a complex number?  
(3) a pure imaginary number?  
(4) represented by a point in the fourth quadrant of the complex plane?

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