We have studied experimentally the responses of high quality single crystals of stoichiometric synthetic magnetite to applied weak dc and ac magnetic fields in the range of 6 K to 60 K, far below the Verwey transition. The results can be compared to so called Magnetic After Effects (MAE) measurements, which are the most extensive magnetic measurements of magnetite at these temperatures. We present a novel point of view on the relaxation phenomena encountered at these temperatures - the Low Temperature Anomaly, addressing the striking difference between the results of conventional ac susceptibility measurements and those accompanying MAE measurements, i.e. periodic excitations with strong magnetic pulses. We also draw a connection between this anomaly and the so called glass-like transition and discuss possible mechanisms responsible for these effects.