
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 the ellipse $E$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ passes through the point $P(2,1)$, and its eccentricity is $\frac{\sqrt{3}}{2}$.

(Ⅰ) Find the standard equation of the ellipse;

(Ⅱ) Let $O$ be the origin of the coordinate system. On the minor axis of the ellipse, there are two points $M$, $N$ satisfying $\overrightarrow{OM} = \overrightarrow{NO}$. The lines $PM$ and $PN$ intersect the ellipse at $A$ and $B$, respectively. Investigate whether the line $AB$ passes through a fixed point. If it passes through a fixed point, find the coordinates of the fixed point; if it does not pass through a fixed point, please explain why.

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