I received the following questions via email, and was not sure if they had been asked or answered here, so I thought I'd cross-post.
Q: If you use an ability that uses your health, what happens when you use the lasts health point? Does your appointment get a point for the endcap? Do you get to finish the action?
A: When you lose your last point of health, you are incapacitated, your turn ends, and the opposing team gets a point. If there are other activities included in the action that require you to not be incapacitated, such as resolving an attack, you do not get to complete them. However, if there are actions that happen in spite of or as a consequence of your incapacitation, you can complete those. For example, The Visionary can make her death attack upon being incapacitated this way, and Tachyon can immediately stand up and take another turn if she was incapacitated as a result of Pushing the Limits.