
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) with an eccentricity of $\frac{1}{2}$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ passing through point $A(2,0)$.
(I) Find the equation of the ellipse (C);
(II) A line (l) passing through the right focus of ellipse (C) intersects the ellipse (C) at two distinct points M and N, and the area of triangle AMN is $\frac{6\sqrt{2}}{7}$. Find the general equation of line (l).

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