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Prompt-LTL extends Linear Temporal Logic with a bounded version of the ``eventually'' operator to express temporal requirements such as bounding waiting times. We study assume-guarantee synthesis for prompt-LTL: the goal is to construct a system such that for all environments satisfying a first prompt-LTL formula (the assumption) the system composed with this environment satisfies a second prompt-LTL formula (the guarantee). This problem has been open for a decade. We construct an algorithm for solving it and show that, like classical LTL synthesis, it is 2-EXPTIME-complete.