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Continuum robots have high degrees of freedom and the ability to safely move in constrained environments. One class of soft continuum robot is the “vine” robot. This type of robot extends from its tip by everting or unfurling new material, driven by internal body pressure. Most vine robot examples store new body material in a reel at their base, passing it through the core of the robot to the tip, and like many continuum robots, steer by selectively lengthening or shortening one side of the body. While this approach to steering and material storage lends itself to a fully soft device, it has three key limitations: (i) internal friction of material passing through the core of the robot limits its length in tortuous paths, (ii) body buckling as the robot's body material is re-spooled at the base can prevent retraction, and (iii) constant curvature steering limits the robot's poses and object approach angles in a given workspace. This letter presents a hybrid soft-rigid robotic system comprising a soft vine robot body and a rigid, mobile, internal steering-reeling mechanism (SRM); this SRM is equipped with a reel for material storage, a bending actuator for steering, and is capable of actuating the robot at any point along its length. This hybrid configuration increases reach along tortuous paths, allows retraction, and increases the workspace. We describe the motivation for the device, generate its mathematical models, present its methods of operation, and verify experimentally the models we developed and the performance improvements over previous vine robots.