
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
Let $F\_1$ and $F\_2$ be the left and right foci of the ellipse $(C): \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, respectively. $M$ is a point on $(C)$ and $MF\_2$ is perpendicular to the $x$-axis. The line $MF\_1$ intersects $(C)$ at another point $N$.
(I) If the slope of the line $MN$ is $\frac{3}{4}$, find the eccentricity of $(C)$;
(II) If the sum of the distances from $M$ to $F\_1$ and $F\_2$ is 4, find the equation of the ellipse $(C)$.

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