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Weakly-supervised temporal action localization aims to recognize and localize action segments in untrimmed videos given only video-level action labels for training. Without the boundary information of action segments, existing methods mostly rely on multiple instance learning (MIL), where the predictions of unlabeled instances (i.e., video snippets) are supervised by classifying labeled bags (i.e., untrimmed videos). However, this formulation typically treats snippets in a video as independent instances, ignoring the underlying temporal structures within and across action segments. To address this problem, we propose \system, a novel WTAL framework that enables explicit, action-aware segment modeling beyond standard MIL-based methods. Our framework entails three segment-centric components: (i) dynamic segment sampling for compensating the contribution of short actions; (ii) intra- and inter-segment attention for modeling action dynamics and capturing temporal dependencies; (iii) pseudo instance-level supervision for improving action boundary prediction. Furthermore, a multi-step refinement strategy is proposed to progressively improve action proposals along the model training process. Extensive experiments on THUMOS-14 and ActivityNet-v1.3 demonstrate the effectiveness of our approach, establishing new state of the art on both datasets. The code and models are publicly available at~\url{https://github.com/boheumd/ASM-Loc}.