Event-based Action Recognition (EAR) possesses the advantages of high-temporal resolution capturing and privacy preservation compared with traditional action recognition. Current leading EAR solutions typically follow two regimes: project unconstructed event streams into dense constructed event frames and adopt powerful frame-specific networks, or employ lightweight point-specific networks to handle sparse unconstructed event points directly. However, such two regimes are blind to a fundamental issue: failing to accommodate the unique dense temporal and sparse spatial properties of asynchronous event data. In this article, we present a synergy-aware framework, i.e., EventCrab, that adeptly integrates the"lighter"frame-specific networks for dense event frames with the"heavier"point-specific networks for sparse event points, balancing accuracy and efficiency. Furthermore, we establish a joint frame-text-point representation space to bridge distinct event frames and points. In specific, to better exploit the unique spatiotemporal relationships inherent in asynchronous event points, we devise two strategies for the"heavier"point-specific embedding: i) a Spiking-like Context Learner (SCL) that extracts contextualized event points from raw event streams. ii) an Event Point Encoder (EPE) that further explores event-point long spatiotemporal features in a Hilbert-scan way. Experiments on four datasets demonstrate the significant performance of our proposed EventCrab, particularly gaining improvements of 5.17% on SeAct and 7.01% on HARDVS.