later on不对
英语里一个句子只能有一个谓语动词(动词原形/过去式/第三人称单数都是谓语动词).
and then里面and是并列连词,并列连词的作用就是连接并列成分,在这里它连接了两个并列的句子,既然是两个句子,那整句话出现两个谓语(listened,took)很正常.
而later on不是连词,不能连接句子,那整句话里出现两个谓语部分就不行了. 如果想用later on,可以把原句拆成两个句子,这样就保证了一句话一个谓语,可以说成:
He listened to the tape for half an hour. Later on(,) he took a bath.
或者仍用并列连词and来连接并列句,说成:
He listened to the tape for half an hour, and later on(,) he took a bath.