ComboBox的MVVM绑定SelectedIndex，组合框使用ControlTemplate，绑定不起作用

public class MyViewModel : INotifyPropertyChanged
{
    private int _selectedIndex;
    
    public int SelectedIndex
    {
        get { return _selectedIndex; }
        set
        {
            if (_selectedIndex != value)
            {
                _selectedIndex = value;
                OnPropertyChanged(nameof(SelectedIndex));
            }
        }
    }
    
    public event PropertyChangedEventHandler PropertyChanged;
    
    protected virtual void OnPropertyChanged(string propertyName)
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    }
}

<Window x:Class="MyApp.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:local="clr-namespace:MyApp"
        Title="My App" Height="450" Width="800">
    <Window.DataContext>
        <local:MyViewModel />
    </Window.DataContext>
    <Grid>
        <ComboBox SelectedIndex="{Binding SelectedIndex}">
            <ComboBox.ItemTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding}" />
                </DataTemplate>
            </ComboBox.ItemTemplate>
            <ComboBox.Items>
                <sys:String>Option 1</sys:String>
                <sys:String>Option 2</sys:String>
                <sys:String>Option 3</sys:String>
            </ComboBox.Items>
        </ComboBox>
    </Grid>
</Window>