As a former (2x!) low-carber, I don’t really see how committing to LC at induction-style levels for 4 weeks is going to do you any good. I can tell you unequivocally that if you go back to your normal ways afterwards you’ll gain all the weight back (even if you did it for 4 months, really). Low carb needs to be thought of as a lifestyle with permanent changes, not a quick fix for anything.
I do assume, though, you’re trying to kickstart some good habits and plan on making permanent changes after 4 weeks are up?
May I suggest Whole30 instead? It’s actually tougher than Atkins - no dairy, no soy, no peanut butter, no sulfates - and really gets you in tune with cooking with rules and does help you see how your body does with no food additives and stuff. But also it’s made to only be followed for 30 days. It’s not necessarily
Here’s one article with a bit of an outline. You can google it and find a ton more info. Of course there’s an official site (with stuff to buy!) and a book but you can get enough info online to not need that stuff.
I’ve done low carb, as I said I did it twice for a couple years at a time, and it’s great and I learned a ton and of course have been able to take all those habits and translate them in to some lifelong habits and tricks. I also did Whole30 once and it was a good experience, and was much harder, but it was meant to only be a short, intense crash course in clean eating. I think Whole30 might better suit your needs.