
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 the complex number $Z = (m^2 + 5m + 6) + (m^2 - 2m - 15)i$, for what values of the real number $m$ does:

(1) $Z$ become a real number;  
(2) $Z$ become a pure imaginary number;  
(3) The point corresponding to the complex number $Z$ lie in the fourth quadrant.

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