
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 $C:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with left and right foci $F_{1}, F_{2}$, the focal distance is $6$ and the perimeter is $16$.

(I) Find the equation of the ellipse $C$.

(II) Find the midpoint coordinates of the line segment obtained by intersecting the ellipse $C$ with the line $l$ passing through the point $(3,0)$ with a slope of $\frac{4}{3}$.

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