
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
Let \\(A=\\{x|x^{2}-ax+a^{2}-19=0\\}\\), \\(B=\\{x|x^{2}-5x+6=0\\}\\), \\(C=\\{x|x^{2}+2x-8=0\\}\\).  
\\((1)\\) If \\(A=B\\), find the value of the real number \\(a\\);  
\\((2)\\) If \\(\varnothing \subset A \cap B\\) and \\(A \cap C = \varnothing\\), find the value of the real number \\(a\\).

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