
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 with its foci on the $x$-axis, a short axis length of $4$, and an eccentricity of $\frac{\sqrt{5}}{5}$.
(1) Find the standard equation of the ellipse;
(2) If a line $l$ passes through the left focus of the ellipse and intersects the ellipse at points $M$ and $N$ such that $|MN| = \frac{16}{9}\sqrt{5}$, find the equation of line $l$.

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