I have a similar post on this on StackOverflow but perhaps my misunderstanding is more substantial.
I have an action Index() and an Index view its rendering.
From Index()
Additional to accepted answer when you are in need to change action as well as Controller too:
$('#go_button').click(function() {
$('form').attr("action", "@("Search","OtherControllerName")"); //change the form action
$('form').submit(); // submit the form
});