
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 equation of circle $C$ is $x^{2}+y^{2}=4$, point $P$ is any moving point on circle $C$. A perpendicular line to the $x$-axis is drawn from point $P$, and its foot is $H$. It is also given that $\overrightarrow{OQ}= \dfrac {1}{2}( \overrightarrow{OP}+ \overrightarrow{OH})$, where the moving point $Q$ traces path $E$. The trajectory $E$ intersects the positive $x$-axis and $y$-axis at points $A$ and $B$, respectively; the line $y=kx(k > 0)$ intersects line $AB$ at point $D$, and intersects trajectory $E$ at points $M$ and $N$.  
(Ⅰ) Find the equation of trajectory $E$;  
(Ⅱ) Find the maximum area of quadrilateral $AMBN$.

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