Problem

Source: Polish Mathematical Olympiad finals 2021 P5

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A convex hexagon $ABCDEF$ is given where $ \measuredangle FAB + \measuredangle BCD + \measuredangle DEF = 360^{\circ}$ and $ \measuredangle AEB = \measuredangle ADB$. Suppose the lines $AB$ and $DE$ are not parallel. Prove that the circumcenters of the triangles $ \triangle AFE, \triangle BCD$ and the intersection of the lines $AB$ and $DE$ are collinear.