Ponder, with 'ON' is an activity that involves deep thought and consideration. Dwelling ON something is to think about it for a long period of time, while brooding is to think about something in a gloomy or sullen manner. To MUSE is to PONDER or reflect upon something, while to CHEW ON something is to think about it deeply and carefully. All of these activities are related to the term 'PONDER', with 'ON' being the preposition that ties them together.