Asserting something is an example of verbal behaviour. Arguably, all verbal behaviour is mental behaviour: a behaviour does not count as verbal unless it is done with understanding, and understanding is a mental phenomenon. On this view, mere production of noise does not count as verbal behaviour, no matter how much it sounds like it (so parrots do not exhibit verbal behaviour).
(The inferences need not be made consciously, and might be made extremely quickly.)
An illustrative analogy: Wittgenstein's boxes. We all have a box with something inside. We can look inside our own box, but not in anyone else's. Instead, we can give each other signals about what is in our box. Can we ever know what is in each other's box? Problem: how do I know what your signals mean? You cannot tell me, because that would be just giving more signals.
Response: Surface appearances can be misleading. When I say 'The average Australian family has 2.2 children' I seem to be talking about a thing called 'the average Australian family', but arguably I am not (plausibly, ‘The average Australian family has 2.2 children’ means ‘On average, Australian families have 2.2 children’).
1 entails 2, but not vice-versa. 2 entails 3, but not vice-versa. 3 entails 4, but not vice-versa. The first claim is logical behaviourism. The second claim is sometimes called ontological behaviourism.