
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 $O: x^{2}+y^{2}=1$ passes through the endpoints of the minor axis of ellipse $C: \dfrac{x^{2}}{a^{2}}+ \dfrac{y^{2}}{b^{2}}=1 (a > b > 0)$. Points $P$ 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) Draw a tangent line from point $(0,t)$ to circle $O$ that intersects 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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