
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 $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, with eccentricity $\frac{\sqrt{3}}{2}$, and its two foci are $F_1$ and $F_2$. A line passing through $F_1$ intersects the ellipse $C$ at points $M$ and $N$, and the perimeter of $\triangle MF_2N$ is $8$.
(Ⅰ) Find the equation of the ellipse $C$;
(Ⅱ) If $|MN| = \frac{8}{5}$, find the area of $\triangle MF_2N$.

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