
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 its upper vertex at $(0,2)$ and an eccentricity of $\frac{\sqrt{5}}{3}$.
(1) Find the equation of ellipse $C$;
(2) From a point $P$ on the ellipse $C$, draw two tangent lines to the circle $x^{2}+y^{2}=1$, with the tangent points being $A$ and $B$. When the line $AB$ intersects the $x$-axis and $y$-axis at points $N$ and $M$, respectively, find the minimum value of $|MN|$.

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