
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
Find the real number \\(a\\) for which the complex number \\(z=(a^{2}-2a-3)+(a^{2}+a-12)i\\) satisfies:  
(I) \\(z\\) is a real number;  
(II) \\(z\\) is a pure imaginary number;  
(III) \\(z\\) is located in the fourth quadrant.

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