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We consider a cooperative relay system with multiple users sending packets to a single destination in a two-phase transmission scheme. In the first phase, users broadcast their packets to the destination via independent channels and attempt to receive packets transmitted by other users. Assuming the ACK/NAK feedback from the destination is received by all users, users act as relays in the second phase to forward the negatively acknowledged packets they received correctly in the first phase to the destination. We show that by making use of the knowledge of the number of ACK and NAK packets, users can optimize their transmit power levels accordingly to lower the outage probability under an average power constraint. In particular, we derive analytically the optimal power allocation, as a function of the number of acknowledged packets, to minimize the outage probability. We compare the performance achieved by the optimal power allocation to those achieved by other transmit power strategies with the same average power constraint and find that adaptively setting the transmit power based on number of acknowledged packets can improve the outage probability performance significantly.