A computer-implemented technique is described herein that receives captured stroke information when a user enters a handwritten note using an input capture device. The technique then analyzes the captured stroke information to produce output analysis information. Based on the output analysis information, the technique modifies the captured stroke information into an actionable form that contains one or more actionable content items, while otherwise preserving the original form of the captured stroke information. The technique then presents the modified stroke information on a canvas display device. The user may subsequently activate one or more actionable content items in the modified stroke information to perform various supplemental tasks that pertain to the handwritten note. In one case, for example, the technique can recognize the presence of entity items and/or list items in the note and then reproduce them in an actionable form.