How can I interact with my Xamarin Forms App from a referenced Xamarin Forms Class Library?

I have the following projects:

• Cross Platform App (Xamarin.Forms - PCL): "MyApp"
• Class Library (Xamarin.Forms): "MyLibrary"

"MyApp" references the "MyLibrary" assembly. "MyLibrary" contains various methods that interface with our "in-house" Authentication WebAPI. I've managed to get the authentication working- but now I would like to affect our app's UI from within the class library...

How can I (for example) open an alert or change the Application.Current.MainPage from within "MyLibrary"?

I've tried the following:

MyApp - App.xaml.cs

using MyApp.Views;
using Xamarin.Forms;
using Xamarin.Forms.Xaml;

[assembly: XamlCompilation(XamlCompilationOptions.Compile)]
namespace MyApp
{
    public partial class App : Application
    {
        public MyLibrary.MyLibraryThing MyLibraryThing;

        public App()
        {
            MyLibraryThing = new MyLibrary.MyLibraryThing();

            InitializeComponent();

            SetMainPage();
        }

        public static void SetMainPage()
        {
            Current.MainPage = new MainPage();
        }

        protected override void OnStart()
        {
            MyLibraryThing.DoSomething();
        }
    }
}

MyLibrary - MyLibraryThing.cs

using Xamarin.Forms;

namespace MyLibrary
{
    public class MyLibraryThing()
    {
        Application myApp;

        public MyLibraryThing(Application application)
        {
            myApp = application;
        }

        public void DoSomething()
        {
            myApp.Current.MainPage = new ContentPage()
            {
                Content = new Label
                {
                    Text = "Created by MyLibrary.MyLibraryThing.DoSomething()!",
                    VerticalOptions = LayoutOptions.CenterAndExpand,
                    HorizontalOptions = LayoutOptions.CenterAndExpand
                }
            };
        }

        public async void DoSomethingElse()
        {
            await myApp.MainPage.DisplayAlert("Alert", "This alert was created by MyLibrary.MyLibraryThing.DoSomethingElse()!", "Cool");
        }
    }
}

The above produces the following exception:

System.Reflection.TargetInvocationException: Exception has been thrown by the target of an invocation. ---> Java.Lang.RuntimeException: Can't create handler inside thread that has not called Looper.prepare()

How can I make my Application object accessible to my external class library?