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Geometry Level 4

In the diagram, \(AC=1\), where \(C\) is the midpoint of side \(AB\) of triangle \(ABJ\). Square \(BCDE\) is drawn, where \( D\) lies on side \(AJ \) and \(E\) is in the interior of the triangle. Square \(FGIH \) is drawn, where \( G\) lies on side \( BJ\), \(H\) lies on side \(AJ\), \(I\) is in the interior of the square, and \( E\) is the midpoint of \(FG\).

Find the area of triangle \(ABJ \).

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