Before discovering the first exoplanets, the radial velocity (RV) method had been used for decades to discover binary stars. Despite the significant advancements made with this technique, it is limited by the maximum accuracy we can reach, the need for long-term observational campaigns that are often hard to keep going, and the mass-inclination degeneracy. For this reason, combining it with astrometry and direct imaging can greatly increase what we can learn about systems with substellar companions having very long periods. HD 72659 is an old solar analog known to host a gas giant on a ~10-yr orbit discovered in 2003 and a very massive outer companion. This work aims to confirm HD 72659 c, which was recently announced using data from the High- Resolution Echelle Spectrometer (HIRES) and the High Accuracy Radial velocity Planet Searcher (HARPS) instruments. We monitored HD 72659 with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) in the framework of the Global Architecture of Planetary Systems (GAPS) project since 2012 and now combined our large data set with literature data, Gaia DR3 high-precision astrometry, and a high-resolution imaging observation taken with SPHERE (Spectro-Polarimetric High-contrast Exoplanet REsearch) to accurately constrain the mass and the orbit of this object (M_c_~19M_Jup}, a~21au) that falls in the so-called Brown Dwarf desert. We characterize the orbital parameters of HD 72659 c, confirming the literature mass of this object but not the period, and we also refine the parameters of planet b with reduced error bars compared to previous works. Finally, since this star hosts two massive objects with long orbital periods, the innermost one having moderate eccentricity, we analyze and discuss the dynamic configuration of this peculiar case, finding that the Kozai-Lidov may be at work in this system.