
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 C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$), one of the vertices of the short axis and the two foci form a right-angled triangle, and the area of the triangle is 1.
(Ⅰ) Find the equation of ellipse C;
(Ⅱ) Let $F_1$ and $F_2$ be the left and right foci of ellipse C, respectively. Two parallel lines passing through $F_1$ and $F_2$ intersect the ellipse at four distinct points A, B, C, and D. Find the maximum area of quadrilateral ABCD.

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