
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 the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) and a hyperbola with the equation $\frac{x^2}{3} - y^2 = 1$, the eccentricities of which are reciprocals of each other. The line $x - y - 2 = 0$ passes through the right vertex of the ellipse.
(I) Find the standard equation of the ellipse (C);
(II) Let a line not passing through the origin O intersect the ellipse (C) at points M and N, and the slopes of the lines OM, MN, ON form a geometric sequence. Find the range of the area of triangle OMN.

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