
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: \\(\\frac{{{x}^{2}}}{{{a}^{2}}}+\\frac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)\\) with an eccentricity of \\(\\frac{\\sqrt{3}}{2}\\), a long axis length of \\(4\\sqrt{2}\\), and point _\\(C(2,1)\\)_ with its symmetric point about the coordinate origin being _\\(D\\)_.

(I) Find the equation of the ellipse.

(II) A line \\(l\\) parallel to _\\(CD\\)_ intersects the ellipse at points _\\(M\\)_ and _\\(N\\)_. When the area of triangle \\(\\Delta CMN\\) reaches its maximum value, find the equation of line \\(l\\).

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