Online social networks have increased their impact on the real world, which motivates information senders to control the propagation process of information to promote particular actions of online users. However, the existing works on information provisioning seem to oversimplify the users' decision-making process that involves information reception, internal actions of social networks, and external actions of social networks. In particular, characterizing the best practices of information provisioning that promotes the users' external actions is a complex task due to the complexity of the propagation process in OSNs, even when the variation of information is limited. Therefore, we propose a new information diffusion model that distinguishes user behaviors inside and outside of OSNs, and formulate an optimization problem to maximize the number of users who take the external actions by providing information over multiple rounds. Also, we define a robust provisioning policy for the problem, which selects a message sequence to maximize the expected number of desired users under the probabilistic uncertainty of OSN settings. Our experiment results infer that there could exist an information provisioning policy that achieves nearly-optimal solutions in different types of OSNs. Furthermore, we empirically demonstrate that the proposed robust policy can be such a universally optimal solution.