The first one is not proper JSF action invocation and if it works at all, it would only be because EL made it work, not JSF.
The second one will probably work. Try it. If it doesn't then you either are going to need to code an additional action method somewhere that calls the 2 methods or you'd have to use a set of ActionListeners. But let's hope you don't need listeners, since they would require recoding your backing-bean methods.
Customer surveys are for companies who didn't pay proper attention to begin with.