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stop an asynchronous operation to start a replacing one
Task currentTask;
CancellationTokenSource cancelTokenSource;
CancellationToken cancelToken;
Task newTask;
CancellationTokenSource newCancelTokenSource;
CancellationToken newCancelToken;

public Form1()
{
    InitializeComponent();
}

private void button1_Click(object sender, EventArgs e)
{
    if(currentTask != null && currentTask.Status == TaskStatus.Running)
    {
        //Cancel the running task
        cancelTokenSource.Cancel();
        //Prepare a new Task to be triggered when the other cancels
        //You could store new tasks/tokens in a dictionary if you wanted,also
        //A new cancel token is always needed since the old stays cancelled
        newCancelTokenSource = new CancellationTokenSource();
        newCancelToken = newCancelTokenSource.Token;
        newTask = new Task(()=>LongRunningTask(), newCancelToken);

        //Continue that deals with both cancel and completion
        //There is a different way to deal with this below, also
        newTask.ContinueWith((previousTask)=>
        {
            if(previousTask.Status == TaskStatus.Cancelled)
            {
                label1.Text = "New Task Cancelled, Another New Starting";
                BeginNewTask();
            }
            else
                label1.Text = "New Task Ran To Completion";
        },
        //If cancelled token is passed, it will autoskip the continue
        new CancellationTokenSource().Token, TaskContinuationOptions.None,
        //This is to auto invoke the UI thread
        TaskScheduler.FromCurrentSynchronizationContext());
    }
    else
    {
        cancelTokenSource = new CancellationTokenSource();
        cancelToken = cancelTokenSource.Token;
        //Start a fresh task since none running
        currentTask = Task.Factory.StartNew(()=>LongRunningTask(),
            cancelToken);

        //OnCancelContinue
        currentTask.ContinueWith((previousTask)=>
        {
            label1.Text = "First Task Cancelled, New Starting";
            BeginNewTask();
        },
        //If cancelled token is passed, it will autoskip the continue
        new CancellationTokenSource().Token,
        TaskContinuationOptions.OnlyOnCancelled,
        //This is to auto invoke the UI thread
        TaskScheduler.FromCurrentSynchronizationContext());

        //OnCompleteContinue
        currentTask.ContinueWith((previousTask)=>
        {
            label1.Text = "First Task Ran To Completion";
        },
        //If cancelled token is passed, it will autoskip the continue
        new CancellationTokenSource().Token,
        TaskContinuationOptions.OnlyOnRanToCompletion,
        //This is to auto invoke the UI thread
        TaskScheduler.FromCurrentSynchronizationContext());
    }
}

private void LongRunningTask()
{
     for(int i = 0; i < 60; i++)
     {
         if(cancelToken.IsCancellationRequested)
             cancelToken.ThrowIfCancellationRequested();
         Thread.Sleep(1000);
     }
}

private void BeginNewTask()
{
    //Since the old task is cancelled, reset it with the new one
    //Probably should do some error checks
    currentTask = newTask;
    cancelTokenSource = newCancelTokenSource;
    cancelToken = newCancelToken;
    //This is to make sure this task does not run on the UI thread
    currentTask.Start(TaskScheduler.Default);
}