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Nowadays more and more information systems are being shifted to distributed architectures because of the benefits like scalability, autonomy, and faulty-tolerance implied from the essence of this distributed systems. Here, every process is peer and cooperates with other peers to achieve some objectives. Here, peers have to efficiently and flexibly make an agreement on one value which satisfies an agreement condition. We consider a distributed group of multiple peers with no centralized coordination. In order to efficiently make an agreement, we introduce a novel approach that each peer sends a package of multiple possible values to the other peers at each ongoing round. During the agreement procedure in traditional ways, every peer sends one value to the other peers at each round. It takes time for peers to exchange multiple values with each other and the peers might not be able to make an agreement depending on the order of values shown by the peers. By exchanging packages of values at one round, we can not only increase the possibility that every peer makes an agreement but also reduce the time to reach agreement and the number of messages exchanged among peers. In addition, peers have to efficiently broadcast packages of values to every peer in a group. In this paper, we newly introduce a broadcast message flooding algorithm by taking into account the multipoint relaying (MRPs) mechanism to increase the efficiency of the protocol.