Embodied social agents have recently advanced in generating synchronized speech and gestures. However, most interactive systems remain fundamentally reactive, responding only to current sensory inputs within a short temporal window. Proactive social behavior, in contrast, requires deliberation over accumulated context and intent inference, which conflicts with the strict latency budget of real-time interaction. We present \emph{ProAct}, a dual-system framework that reconciles this time-scale conflict by decoupling a low-latency \emph{Behavioral System} for streaming multimodal interaction from a slower \emph{Cognitive System} which performs long-horizon social reasoning and produces high-level proactive intentions. To translate deliberative intentions into continuous non-verbal behaviors without disrupting fluency, we introduce a streaming flow-matching model conditioned on intentions via ControlNet. This mechanism supports asynchronous intention injection, enabling seamless transitions between reactive and proactive gestures within a single motion stream. We deploy ProAct on a physical humanoid robot and evaluate both motion quality and interactive effectiveness. In real-world interaction user studies, participants and observers consistently prefer ProAct over reactive variants in perceived proactivity, social presence, and overall engagement, demonstrating the benefits of dual-system proactive control for embodied social interaction.