You can use the brace notation for that.
<h:commandButton value="submit" action="#{someBean[headerBean.actionValue]}" />
When the #{headerBean.actionValue} returns a String of for example doAction1, then this will effectively invoke #{someBean.doAction1}.
If the bean name to be called is currently actually in the actionvalue (headerBean.actionValue returning someBean.doAction1), you need to split it into a field that returns the bean name and one that returns the method name and then use
<h:commandButton value="submit" action="#{requestScope[headerBean.beanName][headerBean.actionValue]}" />
If headerBean.beanName returns 'someBean' and headerBean.actionValue returns doAction1 the above will call #{somebean.doAction1}.