The Herrs (Ps) bought lakefront property on Crooked Lake hoping to use the lake's waters for recreational boating and fishing. The United States Forest Service (D) had other plans. Most of Crooked Lake lies in the federally owned Sylvania Wilderness, yet some of it remains under private ownership. Congress gave D the authority to regulate any use of Crooked Lake and nearby lakes 'subject to valid existing rights.' D created two regulations, one prohibiting gas-powered motorboats, the other limiting electrically powered motorboats to no-wake speeds throughout the wilderness area. Crooked Lake stretches three miles from one end to the other connected by a series of meandering channels and bays. The lake offers a variety of outdoor activities for public and private visitors from kayaking to bird watching to hiking along its shore. Fishing apparently attracts a lot of visitors. Ninety-five percent of the land surrounding the lake belongs to the federally protected Sylvania Wilderness. The remaining five percent belongs to approximately ten private landowners who own the property under state law. 'Subject to valid existing rights,' the Michigan Wilderness Act directs D to administer this area 'in accordance with the provisions of the Wilderness Act of 1964.' The Wilderness Act of 1964 addresses motorboat use, explaining that 'subject to existing private rights there shall be no use of motorboats' within any wilderness area. Amendment No. 1 to the plan prohibited the use of sailboats and houseboats on all portions of Crooked Lake within the Sylvania Wilderness. Amendment No. 5, it prohibited the use of 'any motor or mechanical device capable of propelling a watercraft by any means' on the wilderness portion of Crooked Lake. The property owners lost against Amendment no. 1 but won their suit against Amendment no. 5. The district court held that the motorboat restrictions interfered with a ''valid existing right' to use gas motor boats on Crooked Lake' and thus fell outside D's regulatory authority. In 2010, Ps made a commitment to purchase two waterfront lots on the lake's northern bay. Ps bought the land with the intention of using gas-powered motorboats. The seller confirmed these intentions, telling Ps that he had used motorboats in the past 'without hindrance by D.' D regularly sold boating permits to visitors and residents-allowing them access to the lake-and allowed motorboat use through its public boat landing, located in a federally-owned portion of the northern bay just outside the wilderness area. In 2013 D stopped offering motorboat access at the landing dock and sent a letter to Ps informing them that it planned to 'fully enforce' the existing motorboat restrictions on the federal wilderness portion of the lake, though not the private portion of the lake. Ps sued D under the Administrative Procedure Act (APA), seeking to enjoin it from enforcing the motorboat restrictions against them. The district court eventually ruled for D. The court held that Ps' rights to use Crooked Lake did not 'exist' at the time of the Michigan Wilderness Act's enactment, meaning that the reservation of 'valid existing rights' did not apply to them. Ps appealed.