Normally we do not say we are doing an action. Each of those words, do and act, implies the other. If you do something you have acted. If you have acted you have done something.
In some situations, such as your second sentence which is a very nice example, we do want to refer to doing an action but we only need to mention it once. If the teacher was showing a video or a graphic of someone else performing the action we might say she was displaying how to do it. If the teacher is physically performing the action, we would say she is demonstrating how to do it.
The teacher needs to
display/demonstrate how to do the action instead of just telling the students what to do.
Even in the case above the words the action are very vague and generalized. It is a bit odd for me to think of referring to a specific thing using the word the and follow it up with a word as generalized as action. I think in actual conversation I might be apt to select a different word, one that more specifically describes the action.
The teacher needs to demonstrate how to clear the airway instead of just telling the students what to do.
In your question you specifically mention countable actions. Whereas I would be more likely to refer to a specific, countable action by the name of the action itself, clear the airway for example, I would feel comfortable referring to each action or an action as a way to identify an entire, countable series of actions or a non-specific action within that series.
The teacher needs to demonstrate each action instead of just telling the students what to do.