Safe autonomous exploration of unknown environments is an essential skill for mobile robots to effectively and adaptively perform environmental mapping for diverse critical tasks. Due to its simplicity, most existing exploration methods rely on the standard frontier-based exploration strategy, which directs a robot to the boundary between the known safe and the unknown unexplored spaces to acquire new information about the environment. This typically follows a recurrent persistent planning strategy, first selecting an informative frontier viewpoint, then moving the robot toward the selected viewpoint until reaching it, and repeating these steps until termination. However, exploration with persistent planning may lack adaptivity to continuously updated maps, whereas highly adaptive exploration with online planning often suffers from high computational costs and potential issues with livelocks. In this paper, as an alternative to less-adaptive persistent planning and costly online planning, we introduce a new proactive preventive replanning strategy for effective exploration using the immediately available actionable information at a viewpoint to avoid redundant, uninformative last-mile exploration motion. We also use the actionable information of a viewpoint as a systematic termination criterion for exploration. To close the gap between perception and action, we perform safe and informative path planning that minimizes the risk of collision with detected obstacles and the distance to unexplored regions, and we apply action-aware viewpoint selection with maximal information utility per total navigation cost. We demonstrate the effectiveness of our action-aware proactive exploration method in numerical simulations and hardware experiments.