To troubleshoot why your Smart TV is not recognizing your external hard drive, the following list of steps and actions can be taken:

1. Check that your TV’s USB ports are compatible with your external hard drive.
2. Reboot your Smart TV and external hard drive.
3. Ensure the hard drive’s power cord is securely connected.
4. If your external hard drive requires an additional power source, make sure it is connected and the power is properly working.
5. Format the external hard drive, if not already formatted.