Html.Action is a poorly designed technology. Because in your page Controller you can't receive the results of computation in your Partial Controller. Data flow is only Page Controller => Partial Controller.
To be closer to WebForm UserControl (*.ascx) you need to:
Create a page Model and a Partial Model
Place your Partial Model as a property in your page Model
In this situation you can use it like:
public class MyController : Controller
{
....
public MyController()
{
MyChildController = new MyControllerPartial(this.ViewData);
}
[HttpPost]
public ActionResult Index(MyPageViewModel model)
{
...
int childResult = MyChildController.ProcessSomething(model.MyPartialModel);
...
}
}
P.S. In step 3 you can use Html.Partial("PartialViewName", Model.MyPartialModel, <clone_ViewData_with_prefix_MyPartialModel>). For more details see ASP.NET MVC partial views: input name prefixes