Retry HTTP request from .NET with different proxy server

I can issue HTTP requests through a proxy in a .NET app. There are a number of proxy servers I can use and sometimes one or more will go down. How can I have my app retry the HTTP request using a different proxy? I am open to any suggestion and have heard good things about Polly for adding resiliency.

For my use case, it turns out that I was better off without Polly.

public static string RequestWithProxies(string url, string[] proxies)
{
    var client = new WebClient
    {
        Credentials = new NetworkCredential(username, password)
    };
    var result = String.Empty;

    foreach (var proxy in proxies)
    {
        client.Proxy = new WebProxy(proxy);
        try
        {
            result = client.DownloadString(new Uri(url));
        }
        catch (Exception) { if (!String.IsNullOrEmpty(result)) break; }
    }

    if (String.IsNullOrEmpty(result)) throw new Exception($"Exhausted proxies: {String.Join(", ", proxies)}");
    return result;
}