Just a pentagon!

Geometry Level 5

In the pentagon \(ABCDE\), \(AB=\sqrt{2}\), \(BC=CD\), \(\angle ABE=45^{\circ}\) and \(\angle DBE=30^{\circ}\). Compute the area of the pentagon if a circle of radius 1 can be circumscribed about this pentagon.

The area is in the form \(\frac{a+\sqrt{b}}{c}\), where \(a, b,\) and \(c\) are positive integers. Find the value of \(a+b+c\).

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