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The strongly damped collisions of very heavy nuclei 232Th+250Cf at the energy range of 680-1880 MeV have been studied within the improved quantum molecular dynamics model. The production probability of primary superheavy fragments with Z ≥ 114 (SHFs) for the asymmetric reaction 232Th+250Cf is higher than that for the symmetric reaction 244Pu+244Pu and 238U+238U. The calculated results show that the mass and charge distributions of primary fragments, the excitation energy distribution of SHFs depend on the incident energies strongly. Two stages of the decay process of composite systems are distinguished by very different decay slopes, which imply different decay mechanisms of the composite system. The first stage is for the decay of giant composite systems and the second one corresponds to the decay of fragments of giant composite systems including SHFs through emitting neutron, proton or other charged particles, and also through fission or fragmentation. The slow reduction of SHFs in the second stage seems to be helpful for the survival of primary superheavy fragments.