
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 points M and N are respectively the left and right vertices of the ellipse $$C: \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$$, and F is its right focus. The geometric mean of |MF| and |FN| is $$\sqrt{3}$$, and the eccentricity of the ellipse is $$\frac{1}{2}$$.
(1) Find the equation of ellipse C;
(2) Suppose a line l, which does not pass through the origin O, intersects the ellipse at points A and B. If the slopes of lines OA, AB, and OB form a geometric sequence, find the range of the area of triangle OAB.

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