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The magnetization orientation of the polarizing reference layer would fluctuate between the parallel and antiparallel states when the reference layer loses stability. In this paper, a combined analytical and simulation study is presented to predict the magnetic dynamics of the spin valve element with single-domain magnets as the free and reference layers. We acquire a complete phase diagram that includes the normal spin-torque switching and random magnetization fluctuations by tuning the spin torque strength between the free and reference layers. The phase dynamics strongly depends on the magnetization state of the reference layer, showing that the instability of the reference layer could be responsible for the random fluctuation events.