How can I RedirectToAction within $.ajax callback?

I use $.ajax() to poll an action method every 5 seconds as follows:

$.ajax({
    type: 'GET', url: '/MyController/IsReady/1',
    dataType: 'json', success: function (xhr_data) {
        if (xhr_data.active == 'pending') {
            setTimeout(function () { ajaxRequest(); }, 5000);                  
        }
    }
});

and the ActionResult action:

public ActionResult IsReady(int id)
{
    if(true)
    {
        return RedirectToAction("AnotherAction");
    }
    return Json("pending");
}

I had to change the action return type to ActionResult in order to use RedirectToAction (originally it was JsonResult and I was returning Json(new { active = 'active' };), but it looks to have trouble redirecting and rendering the new View from within the $.ajax() success callback. I need to redirect to "AnotherAction" from within this polling ajax postback. Firebug's response is the View from "AnotherAction", but it's not rendering.