Mavericks handles accessibility on a per-application basis, so instead of enabling assistive devices (option does not even exist) carte-blanche, the app which makes the request shows up in a list in System Preferences > Security & Privacy > Privacy where you can enable the access it’s looking for.
Synergy, however, makes a check for the old style of assistive devices setting and fails to start.
From a terminal:
Then open OSX System Preferences and click Security and Privacy, then Accessibility
Check the checkbox on for Terminal and Synergy.
You can then close Synergy and start it again in the background through the terminal:
I expect this will be fixed in the next release (1.4.16 Beta)