Final answer:
The correct action when a dental scaling instrument breaks is to stop using it, inform the client, and report it to a supervisor, but not to continue using it carefully.
Step-by-step explanation:
While working around tooth #25, if a scaling instrument's working end breaks, the appropriate actions would include everything except for one incorrect action, which is option (c) Continue using the broken instrument carefully. It is important to discontinue using a broken instrument as it can cause harm to both the dental professional and the client. Furthermore, the client should be informed about the incident, and the incident must be reported to the supervisor. Using broken dental instruments can compromise patient safety and is against professional dental practice standards.