<image>As shown in the figure, in the triangular pyramid $$P-ABC$$, $$D$$, $$E$$, and $$F$$ are the midpoints of edges $$PC$$, $$AC$$, and $$AB$$, respectively. It is known that $$PA \perp AC$$, $$PA = 6$$, $$BC = 8$$, and $$DF = 5$$. Prove that:
$$(1)$$ The line $$PA \parallel$$ to the plane $$DEF$$;
$$(2)$$ The plane $$BDE \perp$$ to the plane $$ABC$$.