General:
* Continue
* Go on
* Move on
* Advance
* Progress
* Carry on
More specific:
* Start: Begin, commence, initiate
* Follow through: Execute, implement, pursue
* Move forward: Advance, progress, go ahead
* Continue uninterrupted: Persist, persevere, press on
* Go ahead: Proceed, carry on, move ahead
Formal:
* Progress: Advance, develop, move forward
* Carry out: Execute, implement, perform
* Proceed with: Continue with, go ahead with, pursue
The best synonym depends on the specific situation. Consider the context and the intended meaning when choosing a word.