There's a confusion between training and inference time here. Even if LLMs can't reason during inference time, they may be able to do it during pretraining and

There's a confusion between training and inference time here. Even if LLMs can't reason during inference time, they may be able to do it during pretraining and then you can query the existing reasoning during inference. Inference is more like running an algorithm - in fact it is that (Church-Turing equivalence) - so it's up to you if that is reasoning or not.