
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 that the center of ellipse C is at the origin O, with the right focus at $F(\sqrt{3}, 0)$, and M and N are the left and right vertices of the ellipse C, respectively. Point D is a point on the ellipse C that is different from M and N, and the maximum area of △MND is 2.
(1) Find the standard equation of the ellipse C.
(2) Suppose a line l intersects the ellipse C at points A and B, and the slopes of lines OA, l, and OB are $k_1, k, k_2$ (with $k > 0$) respectively. Let $S$ be the area of △OAB, and $S_1$ and $S_2$ be the areas of the circles with diameters OA and OB respectively. If $k_1, k, k_2$ form a geometric sequence, find the minimum value of $\frac{S_1+S_2}{S}$ and the equation of line l at this time.

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