
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 an ellipse $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$, where $F$ is the right focus, $A$ is the right vertex, and $B$ is the top vertex. It is known that $|AB|= \sqrt {3}|OF|$ and the area of $\triangle A0B$ is $\sqrt {2}$.  
$(1)$ Find the equation of the ellipse;  
$(2)$ Determine whether there exists a point $M$ on the line $y=2$ such that the two tangents from $M$ to the ellipse are perpendicular. If such a point exists, find the coordinates of $M$; if not, explain why.

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