In a video on 'Oxford Online English' channel on YouTube (https://youtu.be/jul2urONzOQ?t=794 ), they said that `
You should write to her and thank her for the present
is a complex sentence. Is it? I think it's not.
You should do two things: you should write to her, you should thank her. The subject is one, which is 'you'. 'Write to her' and thank her' are complements of 'should'. Isn't it so? `