Which triangle center is it?

Geometry Level 4

\(AB=AD=BG \text{, } AC=AH=CF \text{, } BC=BI=CE\).

\(L\) is a midpoint of \(ED\), \(K\) is a midpoint of \(FG\), \(J\) is a midpoint of \(HI\).

What is point \(P\) in \(\triangle ABC\) ?

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