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Time series analytics has been widely applied across various domains. While existing time series foundation models (TSFMs) have demonstrated promising results, they still face two major challenges: 1) Most TSFMs mainly rely on stacking Transformer layers to increase parameter size, lacking the ability to adaptively model complex time series patterns from multi-domain data. 2) Current TSFMs are primarily pre-trained for specific tasks, e.g., forecasting or anomaly detection, and a few models support multiple tasks, but they fail to fully leverage task specificity and commonality, resulting in suboptimal performance. To address these challenges, we propose TimeSeek, a novel generalized time series analytics model that adaptively models time series patterns from multi-domain data and unifies multiple tasks in pre-training. Conceptually, TimeSeek is guided by selective information sharing under domain and task heterogeneity. From the perspective of multi-domain data, we propose a Multi-Domain Feature Extractor that adaptively captures temporal dependencies and channel correlations based on domain-specific characteristics, including progressive multi-scale modeling and adaptive slot channel modeling. From the perspective of the diversity of tasks, we propose multi-task collaborative training, which leverages task specificity and task commonality through task customization and cross-task training, effectively unifying multiple tasks in pre-training and better adapting to diverse downstream scenarios. After pre-training on large-scale time series data, TimeSeek achieves state-of-the-art performance in forecasting, anomaly detection, and classification tasks across both few-shot learning and zero-shot situations, together with favorable inference efficiency.