
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 $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) and a hyperbola $\frac{x^2}{3} - y^2 = 1$ whose eccentricities are reciprocal to each other, and the line $x - y - 2 = 0$ passes through the right vertex of the ellipse.  
(Ⅰ) Find the standard equation of ellipse $C$;  
(Ⅱ) Suppose a line that does not pass through the origin $O$ intersects ellipse $C$ at points $M$ and $N$, and the slopes of lines $OM$, $MN$, and $ON$ form a geometric sequence in order. Find the range of the area of $\triangle OMN$.

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