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This paper investigates an intelligent reflecting surface (IRS)-aided multi-cell multiple-input single-output (MISO) system with several multi-antenna base stations (BSs) each communicating with a single-antenna user, in which an IRS is dedicatedly deployed for assisting the wireless transmission and suppressing the inter-cell interference. Under this setup, we jointly optimize the coordinated transmit beamforming at the BSs and the reflective beamforming at the IRS, for the purpose of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) at the users, subject to the individual maximum transmit power at the BSs and the reflection constraints at the IRS. To solve the non-convex problem, we first present an exact-alternating-optimization design to optimize the transmit and reflective beamforming vectors in an alternating manner, in which the transmit and reflective beamforming optimization subproblems are solved exactly by using the technique of semi-definite relaxation (SDR). However, it has high computational complexity and may lead to compromised performance due to the uncertainty of randomization in SDR. To avoid these drawbacks, we further propose an inexact-alternating-optimization design, in which the transmit and reflective beamforming optimization subproblems are solved inexactly based on the principle of successive convex approximation (SCA). In addition, to further reduce the complexity, we propose a low-complexity inexact-alternating-optimization design, in which the reflective beamforming optimization subproblem is solved more inexactly. Numerical results show that the significant performance gains achieved by the proposed three designs against benchmark schemes. Moreover, the inexact-alternating-optimization designs outperform the exact-alternating-optimization one in terms of both the achieved min-weighted-SINR value and the computational complexity.