
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 the ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{2}=1$ with foci on the $x$-axis, the standard equation of the parabola with the right vertex of the ellipse as the focus is $y^{2}=16x$.
(1) Find the eccentricity of the ellipse $C$.
(2) If the slope of the moving line $l$ is $- \frac{ \sqrt {2}}{2}$, and it intersects the ellipse $C$ at two distinct points $M$ and $N$, with point $Q(- \sqrt {2},0)$, find the minimum value of $\overrightarrow{QM}\cdot \overrightarrow{QN}$.

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