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Magnetic nanoparticles constitute potential nanomedicine tools based on the possibility to obtain different responses triggered by safe remote stimulus. However, such richness can be detrimental if the different performances are not accurately differentiated (and controlled). An example of this is the reorientation of magnetic nanoparticles under the influence of AC fields, which can be exploited for either magneto-mechanical actuation (MMA) at low frequencies (tens of Hz); or heat release at large ones (MHz range). While it is clear that Brownian rotation is responsible for MMA, its heating role in the high-frequency regime is not clear. In this work we aim to shed light on this issue, which needs to be well understood for applications in magnetic fluid hyperthermia (MFH) or heat triggered drug release. Using a Brownian dynamics (BD) simulation technique, we have theoretically investigated the contribution of Brownian reversal in disk-shape particles (to enhance the viscous interaction with the environment) over a wide range of frequencies. Our results predict essentially negligible hysteresis losses both in the high- and low-frequency domains, with completely different implications: highly efficient MMA, but negligible MFH performance. Importantly, complementary micromagnetic simulations indicate that the large magnetic torque assumption of the BD simulations is supported by hexagonal-shape disks, up to field amplitudes of the order of 100 Oe. Larger fields would lead to N\'eel reversal which, noteworthy, predicts significant heating performance. The possibility of switching between the MMA and MFH response by changing the amplitude of the AC field, together with their distinct optimal conditions (large magnetic torque for MMF; large heating for MFH), points to such hexagonal nanodisks as promising nanomedicine agents with double mechanical and heating functionalities., Comment: 26 pages, 6 figures