Is the information sufficient?

Geometry Level 4

In the diagram, AC=1AC=1, where CC is the midpoint of side ABAB of triangle ABJABJ. Square BCDEBCDE is drawn, where D D lies on side AJAJ and EE is in the interior of the triangle. Square FGIHFGIH is drawn, where G G lies on side BJ BJ, HH lies on side AJAJ, II is in the interior of the square, and E E is the midpoint of FGFG.

Find the area of triangle ABJABJ .

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