What do you like to do? Do you like to write code? Do you like to organize the tests? Do you like to manage the situation? Do you really get a kick out of text editors? Do you like certain tools? Is there a process type that you really click with? Do you like process?
What exactly do you mean by specialization? Do you mean develop some new skills? Or do you mean that you'd like to be seen primarily as a specialist with a certain application suite (PeopleSoft, Oracle Apps, SAP, etc.)?
Learning how to use an automation tool and becoming proficient with it is a good transition.
The best thing to do is to take the initiative and just investigate things. Too many testers sit around and wait for training opportunities to arise instead of digging into new technologies and showing some intellectual curiosity. Don't sit on the sidelines wondering what to do.
Look at job descriptions for some of the more senior and high demand Software Test jobs. See what's in the job descriptions and figure out some sort of road map for getting to that level.