<image>Translate the following mathematical problem into English, retaining the  identifier in the text:

As shown in the diagram, it is known that in the quadrangular pyramid $$P-ABCD$$, the base $$ABCD$$ is a square, the side face $$PDC$$ is an equilateral triangle, and plane $$PDC⊥$$ plane $$ABCD$$, $$E$$ is the midpoint of $$PC$$.


$$(1)$$ Prove: $$PA/\!/$$ plane $$BDE$$; $$(2)$$ Prove: plane $$BDE⊥$$ plane $$PBC$$.