Using "Go on"

Go on + gerund means to continue with the action in the gerund.

Examples
  • He went on speaking for two hours.
  • I can't go on working like this - I'm exhausted.
  • Even after I apologized, he went on being angry for another month.
  • The show will go on playing through the end of the year.

Go on + infinitive means to do the next action, which is often the next stage in a process described in the context.

Examples
  • After introducing her proposal, she went on to explain the benefits for the company.
  • John Smith worked in local government for five years, then went on to become a Member of Parliament.
  • After making dinner, I went on to set the table.
  • When you're done with your soup, you can go on to serve the main dish.