
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 ellipse $\Gamma$: $\dfrac {x^{2}}{a^{2}}+y^{2}=1(a > 1)$, its left focus is $F_{1}$, the right vertex is $A_{1}$, and the top vertex is $B_{1}$. The circle $P$ that passes through points $F_{1}$, $A_{1}$, and $B_{1}$ has its center coordinates at $\left( \dfrac { \sqrt {3}- \sqrt {2}}{2}, \dfrac {1- \sqrt {6}}{2}\right)$.  
(Ⅰ) Find the equation of the ellipse;  
(Ⅱ) If the line $l$: $y=kx+m$ ($k,m$ are constants, $k\neq 0$) intersects the ellipse $\Gamma$ at two distinct points $M$ and $N$.  
(i) When the line $l$ passes through $E(1,0)$, and $\overrightarrow{EM}+2 \overrightarrow{EN}= \overrightarrow{0}$, find the equation of the line $l$;  
(ii) When the distance from the origin $O$ to the line $l$ is $\dfrac { \sqrt {3}}{2}$, find the maximum area of $\triangle MON$.

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