
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 the parabola \\(C: y^2 = 2px (p > 0)\\) and a point \\((3,m)\\) on \\(C\\) that is 5 units away from the focus \\(F\\).

\\((1)\\) Find the equation of \\(C\\).

\\((2)\\) A line \\(l\\) passes through \\(F\\) and intersects \\(C\\) at points \\(A\\) and \\(B\\). If the y-coordinate of the midpoint of line segment \\(AB\\) is \\(-1\\), find the equation of line \\(l\\).

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