C# State-Pattern private ChangeState

I´m trying to implement the State-Pattern using C# following this page. Here the UML of a State-Pattern.

The State it self sets the new sate in the context class. But here is my problem: I want to use Interfaces but the ChangeState-Method should not be present to the client but available for the state. But I don´t know how to implement a private interface within a class which I present for the client.

Here my first shot of the pattern Context-Class which should implement the IChangeState interface:

public interface IContext 
{
    string Input { get; set; }
    void DoTransition();
}

public class Context : IContext
{ 
    public string Input { get; set; }

    private AbstractState _state;

    public void DoTransition() 
    {
        _state.DoTransition();
    }
}

And the IChangeState interface which does the main trick but should not be visibile to the client. So I assumed to make it private but how to share this interface with the state or even implement it?

public interface IChangeState 
{
    void ChangeState(IState state);
}

And at least the States:

public interface IState 
{
    void DoTransition();
}

public abstract class AbstractState : IState 
{
    private IChangeState _stateChanger;

    public AbstractState(IChangeState stateChanger) => _stateChanger = stateChanger;

    public virtual void DoTransition() 
    {
        _stateChanger.ChangeState(new NextState(_stateChanger));
    }
}

public class NextState : AbstractState 
{
    public NextState(IChangeState stateChanger) 
        : base(stateChanger)
    { }

    public override void DoTransition()
    {
        base.DoTransition();
    }
}