You would use 'continue' if the action has already begun and you stopped for whatever reason. If you had the intention of an action but never started it, then went back to it, you would 'proceed'

These words are synonyms! They have the same usage. I think "proceed" sounds a bit more formal, however.

Hello! My name Alex. I am from Rissia. I live in Moscow!

Hey Kheng. Thank you very much for taking the time to answer my question. I gotta say it was very informative and helped me a lot! I enjoyed the reading. Thanks again!

Hey Andrey, It definitely feels like they are interchangeable in the sense where they show the progress of an activity. However, 'proceed' is often used to illustrate the start of a new activity/action, and cannot be replaced with 'continue' in such contexts. 'The runners continued to run' <- the runners were running before and are still running. 'The runners proceeded to run' <- the runners were not running before but started running OR the runners were running before and are still running. Personally, without given context the first interpretation would come to mind immediately (not so much the second). You can use 'continue' directly before the progressive form of a verb, whereas it feels really unnatural using 'proceed' this way (probably incorrect but I’m not 100% sure): 'let's continue drinking the wine' <- gladly(: vs. 'let's proceed emptying the bottle' <- okay slow down buddy (basically sounds really weird). For describing an action, 'proceed' precedes 'with', 'to' e.g. 'Proceed/ed to empty the bottle'. 'Proceed/ed with emptying the bottle'. 'Continue' can be used in such constructions as well, i.e. 'Continue to empty the bottle'. 'Continue with emptying the bottle'. Take note of the tenses here. Some people use ‘proceed on to/on with’, I’m not sure if this is right. When 'proceed' is used to refer to a noun, it’s (almost) always used with 'with', or 'on with' (example 1). I dare say that 'The board proceeded their meeting after a short break' sounds somewhat unnatural without ’with’ or ‘on with’… 'Continue' usually takes ‘with’, i.e. ‘continue with the meeting’. TLDR; In describing the continuation of an action without a break, 'continue' feels more natural. ‘Proceed’ makes it sound like the activity just started or that there was a break. Sorry for the long read! Hope I’ve helped you a little