do someone's bidding(U.S. officials who opposed the decision to go after al-Nusra's wider leadership warned that the United States would effectively be doing the Assad government's bidding by weakening a group on the front line of the counter-Assad fight.VLZ_58)
play into one's efforts(Having incompetent enemies is a blessing. For three years, Chinese President Xi Jinping has showered blessings upon the US. A self-isolated, belligerent and increasingly repressive China has been its own worst enemy, playing into America’s efforts to check Chinese power.bloomberg.comaldrignedigen)