How to Avoid Facebook's Creepy Ads Based on Your Offline Purchases

What are the possible mechanisms that allow facebook to target ads based on offline purchases that are not linked to any online account or activity? For example, I bought a specific brand of ice cream with cash at a store, and later saw an ad for the same product on facebook, even though I do not have the facebook app on my phone, nor did I use any other app or browser that could have tracked my location or purchase. Could an app like instagram, which is owned by facebook, access my phone's data or microphone without my permission or knowledge, and transmit it to facebook's servers? Or could there be a connection between the store's point of sale system and facebook's ad network that could identify me based on some unique identifier? How can I prevent this kind of intrusive and unwanted advertising?

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