How to create an Entity Data Model using SQLite in Visual Studio 2013?

Question

SQLite

The problem is that I can't create an *.edmx file that would use a SQLite connection.

As you can see, SQLite providers are missing here, although they are in app.conf!
In order to use EF and SQLite, I installed the SQLite components using Nuget into my project.
There are links to SQLite assemblies in the project.
The .NET and SQLite versions of the components match.
I'm trying to create a model from an existing database that I created using the SQLite browser and it already has one table.
Maybe I'm missing something?