advance: stresses effective assistance in hastening a process or bringing about a desired end: a gesture intended to ~ the cause of peace.
promote: suggests an open encouraging or fostering: a company trying to ~ better health among employees; and may denote an increase in status or rank: a student ~d to third grade. (foster培养,如foster parents养父母)
forward: implies an impetus or moral force moving something ahead: a wage increase would ~ productivity. (impetus推动力,词根PET表示寻找to seek,字面意思是去寻找,如the promise of a nice bonus gave us an impetus for finishing the project on time承诺给我们奖金推动我们按时完成项目,其它PET组成的词有compete竞争,petition情愿,centripetal向心的,appetite食欲,和impetuous冲动草率)
further: suggests a removing of obstacles in the way of a desired advance: used the marriage to ~ his career.