
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
In the rectangular coordinate system $xoy$, there is an ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity of $\frac{1}{2}$. Two chords, $EF$ and $MN$, are drawn through the right focus $F$ of the ellipse, and they are perpendicular to each other. When the slope of $EF$ is $0$, $|EF|+|MN|=7$.
(1) Find the equation of the ellipse $C$;
(2) Find the range of values for $|EF|+|MN|$.

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