The following are perhaps the most likely answers though they are not the only correct ones:

implies: No vegetables are on the boy’s plate

implicates: The boy has finished his vegetables

implies: The trunk is not empty

implicates: There is beer in the cooler

implies: The speaker has seen a movie by the director in question.

implicates: The speaker has not seen the new movie [with further implicatures depending on the tone of voice]

The truth value of I’m Adam depends on features of the context in which it is uttered—specifically, on the identity of the speaker. So, it is not true in some contexts of utterance. And that means that, if we assume it is used correctly, it can tell us something about the context—who the speaker is. We derive this information not simply by assuming that the actual world is a world in which the sentence is true but by assuming, more specifically, that the sentence has been uttered in a context that makes it express a true proposition. And even if it tells us nothing about the actual world to know that the person Adam is himself, it does tell us something about the context to know that the person Adam is the speaker.

If Austin was right, thousands of answers are possible. I will simply note a five-fold classification of speech acts along with examples of performative verbs for each sort of act. (This classification is due to the philosopher John Searle but based on Austin’s ideas.) (1) representatives (e.g., assert and conclude) commit the speaker to the truth of something. (2) directives (e.g., order and ask) are attempts to get the speaker’s audience to do something. (3) commissives (e.g., promise and threaten) commit the speaker to some future action. (4) expressives (e.g., apologize and congratulate) express a psychological state. (5) declarations (e.g., sentence and promote) effect a change in an institution.