
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 $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, the length of the major axis is $\frac{3\sqrt{5}}{5}$ times the length of the minor axis. Let $A$ be the left vertex of the ellipse $C$, $F$ be the right focus of the ellipse $C$, and points $M(x_0, y_0) (x_0 > 0, y_0 > 0)$, $N$ are on the ellipse $C$.
(Ⅰ) If point $D(-1, \frac{2\sqrt{10}}{3})$ is on the ellipse $C$, find the maximum value of $|NF|$;
(Ⅱ) If $\overrightarrow{OM} = 2\overrightarrow{AN}$ ($O$ is the origin), find the slope of line $AN$.

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