
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 value of the real number \\(k\\), is the complex number \\(z=(k^{2}-3k-4)+(k^{2}-5k-6)i\\): \\((1)\\) a real number; \\((2)\\) a complex number; \\((3)\\) a purely imaginary number; \\((4)\\) equal to \\(0\\)?

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