Propose + gerund means suggest. In this formulation, it has the same meaning as when followed by a that-clause.
- John proposed going to the debate.
- I proposed having lunch together.
- Who proposed eating at this restaurant?
- I propose that we buy a smaller car.
- I propose buying a smaller car.
Propose + infinitive means intend or offer.
- The Government proposes to bring in new laws.
- I propose to finish this meeting tomorrow.
- He proposed to go so I didn't have to.
- Janet has proposed to take notes and circulate them afterwards.