Managing user controls from another window in WPF

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C#

I am using WPF, and have a MainWindow.xaml, also I have a user control Page_SwitcherMenu.xaml, practically this is common for other user controls.

I have a label in Page_SwitcherMenu.xaml which monitors network activity, if LAN is down label background turns red.

I need to implement the code in MainWindow.xaml.cs, the label name is lbl_LAN and is located in Page_SwitcherMenu.xaml.

How can I do this? I have tried to use binding but did not manage to.

What I have tried:

MainWindow.xaml.cs contains the following:

public MainWindow()
        {
            InitializeComponent();
            this.WindowStyle = WindowStyle.None;
            this.AllowsTransparency = false;
            PageSwitcher.pageSwitcher = this;
            PageSwitcher.Switch(new Page_Info());

            NetworkChange.NetworkAvailabilityChanged += new NetworkAvailabilityChangedEventHandler(NetworkChange_NetworkAvailabilityChanged);
        }

 void NetworkChange_NetworkAvailabilityChanged(object sender, NetworkAvailabilityEventArgs e)
        {
            GlobalData.NetworkOnline = e.IsAvailable;
            if (GlobalData.NetworkOnline == true)             
               
                lbl_LAN.Background = Brushes.PaleGreen;
            else
                lbl_LAN.Background = Brushes.Red;
        }