I know it's possible to make Apex class methods available as a REST service with annotations. I also know it's possible to make a call to an external web service from an Apex class. Can I combine the two?
Example: I create an Apex class with REST methods. The REST Apex methods within that class in turn calls another third-party web service, gets data, and my Apex REST class returns the results from the third-party web service. I'm trying to wrap the third-party REST call in my Apex class, i.e., make Salesforce the middleman.