
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 a circle \\(C\\): \\(x^{2}+y^{2}+8y+12=0\\), and a line \\(l\\): \\(ax+y+2a=0\\).  
\\((1)\\) For what value of \\(a\\) does line \\(l\\) become tangent to circle \\(C\\);  
\\((2)\\) When line \\(l\\) intersects circle \\(C\\) at points \\(A\\) and \\(B\\), and \\(|AB|=2 \sqrt {2}\\), find the equation of line \\(l\\).

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