
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 circle $O$: $x^{2}+y^{2}=1$ passing through the endpoint of the minor axis of the ellipse $C$: $\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1 (a > b > 0)$, $P$ and $Q$ are any two points on circle $O$ and ellipse $C$, respectively, and the maximum length of segment $PQ$ is $3$.
(I) Find the equation of ellipse $C$;
(II) A tangent line is drawn through point $(0,t)$ on circle $O$ intersecting ellipse $C$ at points $M$ and $N$. Find the maximum area of $\triangle OMN$.

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