<image>(2015 Autumn, Chao Yang District School-Level Monthly Exam) As shown in the figure, in the spatial quadrilateral ABCD, points E, F, and G are on AB, BC, and CD respectively, and satisfy AE:EB=CF:FB=2:1, and CG:GD=3:1. The plane passing through E, F, and G intersects AD at point H.
(1) Find AH:HD;
(2) Prove that EH, FG, and BD are concurrent.