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Visual thinking tools are visualization-enabled mixed initiative systems that empower people in solving complex problems by engaging them in the entire resolution process, suggesting appropriate actions with visual cues, and reducing their cognitive load with visual representations of their tasks. At the same time, the visual interaction style provides an alternative to the dialog-based model employed in most mixed-initiative (MI) systems. Visual thinking tools avoid complex analyses of turn taking, and put users in control all the time. We are especially interested in implementing visual "affordances" in such systems and present three examples used in COMIND, a visual MI system that we have developed. We show how humans can more effectively concentrate on synthesizing problems, selecting resolution paths that were unseen by the machine, and reformulating problems if solutions cannot be found or are unsatisfactory. We further discuss our evaluation of the techniques at the end of the paper.