Are these all OK?
Let's continue our game.
Let's continue our program.
Let's continue our trip / journey.
Let's continue our chat / talk.

Question

Answer

I'm excited to learn more about it. I like to spend my free time playing the game. The game is really very addictive. And I would love to continue it by following the original link https://topcasinosreviews.in/casino/paripesa/, then the game is safe. I found this review on a verified platform. You can check it out.

Answer

The game is really very addictive. And I would love to continue it by following the original link https://topcasinosreviews.in/casino/paripesa/ , then the game is safe. I found this review on a verified platform. You can check it out.

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Yes!  Well done.

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All of these are correct.

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You can use the -ing form as well: 
Let's continue chatting/talking 
Let's continue watching the program/playing that game ("let's continue our game"/"let's pick up from where we left off" would be fine too, left off= stopped) 
Let's continue our journey/trip sounds fine!

Verpassen Sie nicht die Gelegenheit, bequem von zu Hause aus eine Sprache zu lernen. Stöbern Sie in unserer Auswahl an erfahrenen Sprachlehrern und melden Sie sich jetzt zu Ihrer ersten Unterrichtsstunde an!