WE PROPOSE A SERIES OF FOUR 20 KS OBSERVATIONS WITH NUSTAR AND XMM OF THE BINARY X-RAY PULSAR HERCULES X-1. HER X-1 IS A GALACTIC X-RAY BINARY WITH A 35 DAY SUPERORBITAL PERIOD CAUSED BY A WARPED PRECESSING ACCRETION DISK. THE HARD BEAM FROM THE NEUTRON STAR HEATS THIS DISK AND THE CORRESPONDING REPROCESSED THERMAL EMISSION CAN PROVIDE A UNIQUE PROBE OF THE INNER ACCRETION FLOW WITHIN THE PULSAR S MAGNETOSPHERE. THIS ANALYSIS CAN SHED LIGHT ON THE PROCESS OF MAGNETIC ACCRETION WHICH DESPITE BEING RELEVANT TO ACCRETING WHITE DWARFS AND YOUNG STARS IS NOT WELL UNDERSTOOD. OUR PROPOSED ANALYSIS REQUIRES GOOD SPECTRAL AND TIMING RESOLUTION ACROSS THE FULL ENERGY BAND (LESS THAN 1 KEV TO GREATER THAN 20 KEV) IN ORDER TO FULLY CONSTRAIN BOTH THE SOFT EMISSION FROM THE DISK AND THE HARD PULSAR BEAM. ADDITIONALLY CAREFULLY TIMED OBSERVATIONS FROM WITHIN A SINGLE SUPERORBITAL CYCLE ARE NECESSARY TO TRACK THE COMPLETE PRECESSION OF THE DISK. FOR THE FIRST TIME WE WILL TRACK A COMPLETE PRECESSION OF HER X-1 S ACCRETION DISK WITH FULL HARD X-RAY COVERAGE AND GAIN THE CLEAREST PICTURE TO DATE OF THE STRUCTURE AND KINEMATICS OF THE MAGNETIZED ACCRETION FLOW.