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The two constituent beams carry the orbital angular momentum (OAM), which has the same or opposite signs. The resultant patterns exhibit revolving and spinning rotations similar to the Sun-Earth system. The revolving-typed rotation comes of the overall OAM, while the spinning-typed rotation results from the respective OAM of the constituent beam. A kind of soliton patterns can stably exist, for which a vortex is nested centrally in the rotating square-shaped optical envelope and four peaks appear at four corners. The centrally nested vortex splits into two single vortex for r not equal 1, with r being the power ratio between the two constituent beams. The two single vortexes align vertically for r < 1 and horizontally for r > 1, and their spacing increases with vertical bar r - 1 vertical bar. The theoretical results give a possibility of the transforming from cross-phase-typed OAM into the helical-phase-typed OAM, which may find potential applications in beam shaping and controlling. In addition, the square optical envelope may exhibit advantages in the integration of optical components. 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