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In AI research, synthesizing a plan of action has typically used descriptive models of the actions that abstractly specify what might happen as a result of an action, and are tailored for efficiently computing state transitions. However, executing the planned actions has needed operational models, in which rich computational control structures and closed-loop online decision-making are used to specify how to perform an action in a nondeterministic execution context, react to events and adapt to an unfolding situation. Deliberative actors, which integrate acting and planning, have typically needed to use both of these models together -- which causes problems when attempting to develop the different models, verify their consistency, and smoothly interleave acting and planning. As an alternative, we define and implement an integrated acting and planning system in which both planning and acting use the same operational models. These rely on hierarchical task-oriented refinement methods offering rich control structures. The acting component, called Reactive Acting Engine (RAE), is inspired by the well-known PRS system. At each decision step, RAE can get advice from a planner for a near-optimal choice with respect to a utility function. The anytime planner uses a UCT-like Monte Carlo Tree Search procedure, called UPOM, whose rollouts are simulations of the actor's operational models. We also present learning strategies for use with RAE and UPOM that acquire, from online acting experiences and/or simulated planning results, a mapping from decision contexts to method instances as well as a heuristic function to guide UPOM. We demonstrate the asymptotic convergence of UPOM towards optimal methods in static domains, and show experimentally that UPOM and the learning strategies significantly improve the acting efficiency and robustness.