
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 an ellipse \\(C\\) centered at the origin \\(O\\) and passing through point \\(A(2,3)\\), with point \\(F(2,0)\\) as its right focus.

\\((\\)Ⅰ\\()\\) Find the equation of the ellipse \\(C\\);

\\((\\)Ⅱ\\()\\) Is there a line \\(l\\) parallel to \\(OA\\) that intersects the ellipse \\(C\\) at some points, and the distance between line \\(OA\\) and \\(l\\) is equal to \\(4\\)? If it exists, find the equation of line \\(l\\); if not, explain why.

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