Is the information sufficient?

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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