I think we would like to accept (and get a better understanding of) all these answers:
(1) We interact which each other by following some rules.
(2) We share our image of reality.
(3) We reason, or at least offer some basis (or starting point) for reasoning.
(4) We perform some actions, intending to achieve some purposes.
Davidson is concerned with (2) (and the ‘productivity of language’ problem).
Wittgenstein seems to drop (2), but he expands on (1) and (4) by speaking of language games (still, not all games have fixed rules and the term ‘game’ expresses a family-resemblance concept).
Grice talks about (4) by considering the intentions which make the use of a sign into a special action – that of communicating something.
Anscombe provides a better understanding of what it is to have an intention -> Davidson uses some of her thoughts to analyze the concept of action.
Austin and Searle expand mainly on (4), by writing about speech acts.
The problem (for people concerned with keeping (3) in view): if we analyze language in the form of speech acts, then we have to explain how do we reason with speech acts; how do we logically get from a speech act to another and how uttering a speech acts logically prevents us from uttering other speech acts.
Searle and Vanderveken have built a logic for illocutionary acts.
Brandom (if I understood him well) sees (3) as central and then tries to show how we could make (3) and (1) explicit by talking about (4).
A forgotten thought: Wittgenstein: ‘Language meshes with our life.’ – this might be used to keep (2) in view (there is a suggestion for this in Putnam; see also Quine).
Case: biding farewell (as in “preparing to leave”) – unpacking your luggage (as in “preparing to stay”).
These actions seem to oppose each other (although, in a sense, none of them is negative). Doing one of them rationally prevents you from doing the other. This adds to the meaning of biding farewell (unpacking your luggage has no meaning, but we could perhaps speak of some inferential content of non-verbal actions).
We need a theory to tell us what does it mean that some actions rationally oppose each other and some rationally follow from others (or what does it mean that a particular action is a necessary condition for some other action).
To get a better answer to our initial question, one which would expand on (1)-(4), we should be able to extend the application of illocutionary logic to non-verbal actions.
And perhaps we need to distinguish between communicative (verbal) actions and non-communicative (non-verbal) actions in terms of the intentions that accompany them (so that we could explain why some inferential content is communicative and some is not).