
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 vertices at ($-4$,$0$) and ($4$,$0$) respectively, and the minor axis length equal to the focal length.

1. Find the equation of ellipse $C$.
2. If a line $l$ intersects ellipse $C$ at points $M$ and $N$, and the midpoint of segment $MN$ is ($1$,$1$), find $|MN|$.

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