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Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this paper, we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Four feedback configurations are considered: 1) feedback from both receivers to the relay, 2) feedback from each receiver to the relay and to one of the transmitters (either corresponding or opposite), 3) feedback from one of the receivers to the relay, and 4) feedback from one of the receivers to the relay and to one of the transmitters. Our results show that there is a strong motivation for incorporating relaying and feedback into wireless networks.