By Miguel Gutierrez and Dave Graham MEXICO CITY (Reuters) – Mexico's Senate on Wednesday signed off on an energy bill that aims to lure private capital into the state-run oil and gas industry in the biggest shake-up since a 1938 nationalization, sending it to the lower house for debate and final approval. The reform, backed by the ruling Institutional Revolutionary Party, or PRI, and the opposition conservative National Action Party (PAN), will mark the biggest strategic shift since the world's No. 10 oil producer nationalized the sector in 1938. The overhaul is designed to entice private oil companies to either operate independently in Mexico, or partner with state oil giant Pemex through production- and profit-sharing, service contracts and licenses. The Senate approved the bill on Wednesday morning after a marathon overnight debate.