The CARS team was awarded 41 hr of VLA time to study the role of neutral hydrogen in luminous active galaxies. A total of 16 galaxies from our Close AGN Reference Survey will be observed. The observations will provide the deepest H I images ever taken for these luminous nearby AGN down to M(HI)<=1.2e9 Msol/beam. Our observations will allow us to tackle three crucial questions linking luminous AGN and their host galaxies. Namely, we will (i) determine whether suppressed star formation (low H2/HI values), or rather strangulation (high H2/HI values), is at place in nearby luminous AGNs, compared to the non-AGN population at the same stellar mass and morphology stage; (ii) determine what is the dominant gas supply (H2 or HI) for nearby luminous AGN; and (iii) study whether it is AGN feedback, or rather environment, the dominant actor in suppressing star formation.