
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
Let $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ be two points on the ellipse $\frac {y^{2}}{a^{2}}+ \frac {x^{2}}{b^{2}}=1(a > b > 0)$. Given vectors $\overrightarrow{m}=( \frac {x_{1}}{b}, \frac {y_{1}}{a})$ and $\overrightarrow{n}=( \frac {x_{2}}{b}, \frac {y_{2}}{a})$, if $\overrightarrow{m}\cdot \overrightarrow{n}=0$ and the eccentricity of the ellipse is $e= \frac { \sqrt {3}}{2}$ with the minor axis being $2$, and $O$ is the origin of coordinates.

(Ⅰ) Find the equation of the ellipse;

(Ⅱ) Determine whether the area of $\triangle AOB$ is constant. If yes, provide a proof; if not, explain why.

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