如何运行输出文本的流程，并在输出文本时将其写入Javafx textArea？

import javafx.application.Application;
import javafx.application.Platform;
import javafx.scene.Scene;
import javafx.scene.control.TextArea;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;

public class TextOutputExample extends Application {

    private TextArea textArea;

    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage primaryStage) {
        textArea = new TextArea();
        textArea.setEditable(false);

        VBox root = new VBox(textArea);
        Scene scene = new Scene(root, 400, 300);

        primaryStage.setScene(scene);
        primaryStage.show();

        // 在新线程中读取文本并输出到TextArea
        new Thread(() -> {
            try {
                String text = readTextFromFile("example.txt"); // 替换为你的文本来源
                appendTextToTextArea(text);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }).start();
    }

    private String readTextFromFile(String filePath) throws IOException {
        StringBuilder sb = new StringBuilder();
        try (BufferedReader reader = new BufferedReader(new FileReader(filePath))) {
            String line;
            while ((line = reader.readLine()) != null) {
                sb.append(line).append("\n");
            }
        }
        return sb.toString();
    }

    private void appendTextToTextArea(String text) {
        Platform.runLater(() -> textArea.appendText(text));
    }
}