Problem with FOR loop interaction using TStringList

I have TStringList that stores absolute path names of some files and I want to put those names in a text file only if the current checked name does not yet exist inside a text file.

When you perform these steps for the first time, all content in the text list is saved, but when it is run a second time, the second FOR can not check and writes some lines of TStringList that have already been written before , and this time with a few repetitions.

Any suggestions here will be welcome.

Here is my last attempt:

var
  Form1: TForm1;
  ListPathFiles, ListStoredPathFiles: TStringList;
  StoreFile: TextFile;

implementation

{$R *.dfm}

function FileSize(const aFilename: String): Int64;
  var
    info: TWin32FileAttributeData;
  begin
    result := -1;

    if NOT GetFileAttributesEx(PWideChar(aFileName), GetFileExInfoStandard, @info) then
      EXIT;

    result := Int64(info.nFileSizeLow) or Int64(info.nFileSizeHigh shl 32);
  end;

procedure TForm1.btn1Click(Sender: TObject);
var
I, J: Integer;
begin
  I:= 0;
  J:= 0;

if not FileExists('paths.txt') then begin
      AssignFile(StoreFile, 'paths.txt');
      Rewrite(StoreFile);
      CloseFile(StoreFile);
end;

ListPathFiles:= TStringList.Create;
ListStoredPathFiles:= TStringList.Create;

if FileSize('paths.txt') = 0 then
 begin
    ListStoredPathFiles.Add('');
 end;

ListPathFiles.Add('C:\Users\MyUser\Desktop\test\File1.txt');
ListPathFiles.Add('C:\Users\MyUser\Desktop\test\File2.txt');
ListPathFiles.Add('C:\Users\MyUser\Desktop\test\File3.txt');
ListPathFiles.Add('C:\Users\MyUser\Desktop\test\File4.txt');
ListPathFiles.Add('C:\Users\MyUser\Desktop\test\File5.txt');

ListStoredPathFiles.LoadFromFile('paths.txt');

     for I := 0 to ListPathFiles.Count-1 do
      begin

      for J := 0 to ListStoredPathFiles.Count-1 do
       begin
        if Pos(ListPathFiles.Strings[I], ListStoredPathFiles.Strings[J]) > 0  then

        begin
          Break;
        end

        else
         begin

             AssignFile(StoreFile, 'paths.txt');
             Append(StoreFile);
             Writeln(StoreFile, ListPathFiles.Strings[I]);
             CloseFile(StoreFile);

            ShowMessage('New path added in text file!');

          end;

      end;

    end;

    ListPathFiles.Free;
    ListStoredPathFiles.Free;
end;