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The X-ray binary Her X-1 = HZ Her consists of an accreting neutron star and ordinary optical donor star. The 35-day X-ray variability of this system is known since its discovery in 1972 by the UHURU satellite. It was shown previously that this period was caused by forced precession of the warped accretion disk tilted to the orbital plane. In this work we revealed that during the precession cycle variations of the following parameters take place: a) intensity (power) of the stream of matter flowing out of the optical star; b) X-ray luminosity of the neutron star; c) optical flux of the accretion disk; d) X-ray irradiation pattern on the donor star; e) tilt of the inner and outer edge of the accretion disk. The behavior of the variability can be explained by free precession of the neutron star with a period close to the forced one of the accretion disk. The mechanism of synchronization of these periods is discussed.