
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 left and right foci $F_1(-1,0)$ and $F_2(1,0)$ respectively. $M$ is a point on the ellipse such that $MF_2 \perp x$-axis, and the line $MF_1$ intersects the ellipse at another point $N$.
(1) If the slope of the line $MN$ is $\frac {3}{4}$, find the equation of the ellipse $C$;
(2) If $|MN|=5|F_1N|$, find the eccentricity of the ellipse.

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