
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 a circle $C_{1}$ with its center at the origin $O$ and tangent to the line $l_{1}: x-2y+3\sqrt{5}=0$, let point $A$ be a moving point on the circle, $AM\perp x$-axis at point $M$, and the moving point $N$ satisfies $\overrightarrow{MA}= \sqrt{3}\overrightarrow{MN}$. Let the trajectory of the moving point $N$ be curve $C$.  
(Ⅰ) Find the equation of curve $C$;  
(Ⅱ) Line $l$ is perpendicular to line $l_{1}$ and intersects curve $C$ at points $B$ and $D$. Find the maximum value of the area of $\triangle OBD$.

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