Try:
@{Html.RenderAction("Breadcrumb", "Navigation", new {SeoUrl = Model.CarlineBucket.SEOURLName});}
@Html.RenderAction() generates a write call to output something on the page and in your case you are not doing so because RenderAction renders the result directly to the Response.
Instead of
@Html.RenderAction()
Use
@{Html.RenderAction();}