Find a date from a specific list of date

I am a beginner in c # and I can not find the solution for my problem.

I am creating a personal project that allows me to send reminders, I have a date list and I need to do tasks between two specific dates in real life.

I found how to get the next date from today's date but I can't find how to get the previous one

Here is my sample code

void calc_x_date()  
    {
        List<string> x_dates = new List<string>();
        x_dates.Add("10/01/2017");
        x_dates.Add("14/02/2017");
        x_dates.Add("14/03/2017");
        x_dates.Add("11/04/2017");
        x_dates.Add("09/05/2017");
        x_dates.Add("13/06/2017");
        x_dates.Add("04/07/2017");
        x_dates.Add("08/08/2017");
        x_dates.Add("12/09/2017");
        x_dates.Add("10/10/2017");
        x_dates.Add("14/11/2017");
        x_dates.Add("12/12/2017");

        var allDates = x_dates.Select(DateTime.Parse).OrderBy(d => d).ToList();

        var todayDate = DateTime.Today;
        var nextDate = todayDate >= allDates.Last()
             ? allDates.Last()
             : todayDate <= allDates.First()
                 ? allDates.First()
                 : allDates.First(d => d >= todayDate);

       string NextDate = nextDate.ToString(); // the closest next date from today          
       //string PreviousDate =   // the closest previous date from today   
    }

Could someone explain me how to find my previous date please ?

Thanks in advance