
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 \\(E\\): \\(y^{2}=4x\\) with focus \\(F\\), a line \\(l\\) passing through point \\(F\\) intersects the parabola at points \\(A\\) and \\(B\\), and intersects the \\(y\\)-axis at point \\(C\\). Let \\(O\\) be the origin of the coordinates.

\\((1)\\) If \\(k_{OA}+k_{OB}=4\\), find the equation of line \\(l\\);

\\((2)\\) The perpendicular bisector of segment \\(AB\\) intersects line \\(l\\), the \\(x\\)-axis, and the \\(y\\)-axis at points \\(D\\), \\(M\\), and \\(N\\), respectively. Find the minimum value of \\(\dfrac{S_{\triangle NDC}}{S_{\triangle FDM}}\\).

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