Use case help

Hi i am creating a use case for a dental company (courswork) and i was wondering if actions by the system are use cases.

For example: when a patient books an appointment the system using external SMTP sends an email; would there be a use case for this?

Another example when the patients are registering, the system uses CaptureService(those things where you have to type in random letters to prove you’re not a robot/hacker or you know) to validate the registration hence the system will "requestCaptureString"
would this a use case?

Please help asap thanks

A use case = a task/goal

so in your example

“a patient books an appointment the system using external SMTP sends an email”

you can extract the actor “Patient” and his goal is to “create an appointment”

one of the business rules is that a email is send when a task is done ( a appointment is created)