Geometry Level 5

Consider a square $$ABCD$$ with side of length $$4$$.

Let $$E$$ be a point outside $$ABCD$$ such that $$\Delta CDE$$ is equilateral.

Draw $$\angle CEK = 30^\circ$$ such that ray $$EK$$ intersects ray $$AC$$ at $$G$$, ray $$DC$$ at $$F$$, ray $$AB$$ at $$P$$.

If Area of $$\Delta AGP$$ can be represented as:

$a + b\sqrt{c}$ where $$c$$ is independent of a perfect square.

Find $$a + b + c$$.

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