I'm going to Hualian, Taipei, Nantou, Taiwan for the new year, can you give me a route suggestion?

If you fly to Taipei, you can spend two days in Taipei, then take the high-speed rail to Taichung, then transfer to Nantou Sun Moon Lake in the direction of Alishan, return to Taichung the next day, take the high-speed rail to Kaohsiung, and stay in Kaohsiung for a day to visit Cijin. Then take the Taiwan Railway to Hualien and finally return to Taipei.