Police Officers Can Legally Tow and Impound Vehicles for Many

Police officers can legally tow and impound vehicles for many reasons, including vehicles involved in accidents, parked in a tow-away zone, or abandoned on the highway. When the police impound a vehicle for legitimate reason, they may lawfully conduct an inventory search. Assume a police officer lacks probable cause but has a "gut feeling" that a known malcontent from the community has marijuana in the trunk of his car. The police officer follows the malcontent until she fails to stop completely at a stop sign. The police officer pulls over at the malcontent and, after asking for license and registration, finds out (as she already suspected) that the malcontent has a suspended license. The police officer arrests the malcontent and puts her in the backseat of her police car. She then calls the local tow company to impound the vehicle for the owner's safety. The police officer is then happy to hear that during a normal inventory inspection of the vehicle, marijuana is found and she promptly informs the district attorney's office. If the police officer has done nothing that violates the law or the Fourth Amendment, can you articulate an argument that challenges what the police officer did?