Machine Ethics (ME) is concerned with the design of Artificial Moral Agents (AMAs), i.e. autonomous agents capable of reasoning and behaving according to moral values. Previous approaches have treated values as labels associated with some actions or states of the world, rather than as integral components of agent reasoning. It is also common to disregard that a value-guided agent operates alongside other value-guided agents in an environment governed by norms, thus omitting the social dimension of AMAs. In this blue sky paper, we propose a new AMA paradigm grounded in moral and social psychology, where values are instilled into agents as context-dependent goals. These goals intricately connect values at individual levels to norms at a collective level by evaluating the outcomes most incentivized by the norms in place. We argue that this type of normative reasoning, where agents are endowed with an understanding of norms' moral implications, leads to value-awareness in autonomous agents. Additionally, this capability paves the way for agents to align the norms enforced in their societies with respect to the human values instilled in them, by complementing the value-based reasoning on norms with agreement mechanisms to help agents collectively agree on the best set of norms that suit their human values. Overall, our agent model goes beyond the treatment of values as inert labels by connecting them to normative reasoning and to the social functionalities needed to integrate value-aware agents into our modern hybrid human-computer societies.