Agent-based models of financial markets usually make assumptions about agent's preferred stylized strategies. Empirical validations of these assumptions have not been performed so far on a full-market scale. Here we present a comprehensive study of the resulting strategies followed by the firms which are members of the Spanish Stock Exchange. We are able to show that they can be characterized by a resulting strategy and classified in three well-defined groups of firms. Firms of the first group have a change of inventory of the traded stock which is positively correlated with the synchronous stock return whereas firms of the second group show a negative correlation. Firms of the third group have an inventory variation uncorrelated with stock return. Firms tend to stay in the same group over the years indicating a long term specialization in the strategies controlling their inventory variation. We detect a clear asymmetry in the Granger causality between inventory variation of firms and stock return. We also detect herding in the buying and selling activity of firms. The herding properties of the two groups are markedly different and consistently observed over a four-year period of trading. Firms of the second group herd much more frequently than the ones of the first group. Our results can be used as an empirical basis for agent-based models of financial markets.