JavaFX:使用带有ChangeListener的StringProperty根据TimerTask定期更新标签

我正在尝试使用TimerTask每秒更新一次标签,它会更改StringProperty的值:

public class RandomString extends TimerTask {

private StringProperty randomString;
private ArrayList<String> strings;
private Random random;

public RandomString(String... str) {
    randomString = new SimpleStringProperty(this, "randomString", "");
    strings = new ArrayList<>(Arrays.asList(str));
    random = new Random();
}

public String getRandomString() {
    return randomString.get();
}

public StringProperty randomStringProperty() {
    return randomString;
}

public void setRandomString(String randomString) {
    this.randomString.set(randomString);
}

@Override
public void run() {
    int i = random.nextInt(strings.size());
    setRandomString(strings.get(i));
}

public void startTimer() {
    new Timer(true).schedule(this, 0, 1000);
}

为了更新标签,我在StringProperty中添加了一个ChangeListener,它根据字符串更改标签的文本:

randomString.randomStringProperty().addListener(
            (observable, oldValue, newValue) -> 
                    Platform.runLater(() -> label.setText(newValue)
));

但由于我必须使用runLater方法运行此操作,因此标签不会定期更新。如何实现每秒更新一次?