
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
Is there a line \\(l\\) that simultaneously satisfies the following two conditions: \\((1)\\) Line \\(l\\) intersects the parabola \\(y^{2}=8x\\) at two distinct points \\(A\\) and \\(B\\); \\((2)\\) The segment \\(AB\\) is perpendicularly bisected by the line \\(l_{1}\\): \\(x+5y-5=0\\)? If it does not exist, explain why. If it exists, find the equation of line \\(l\\).

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