Moudim D'Rabbonon

Why does one bow both at the beginning of Moudim D'Rabbonon "Moudim Anachnu Loch" and for the word "Boruch" at the end?

Rallis

R' Hamburger explained to me that the beginning of Modim corresponds to the regular Modim - so we bow; the "baruch" at the end corresponds to "baruch...hatov shimcha..." so we bow there also. He told me that according to some (I believe he mentioned the Gra) it is actually Baruch atah Hashem kel haodaos.

Daniel