The sentence source as “A English Practical Grammar, Let’s proceed with SIMPLE ENGLISH”.
Begin a course of action. “the consortium could proceed with the plan” synonyms: begin, make a start, get going, move, take action, act, make progress.
“she was still uncertain how to proceed”
2. Go ahead, carry on, go on, continue, get on, get ahead, prosecute, move forward, get going, keep going, or execute.
Start or continue an action or process. “the building project is proceeding smoothly”.
You should ask a lawyer for advice on how to proceed”. To proceed is also to move forward or travel in a particular direction“. If you proceed to do something, you go on to do it”.