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Human Action Recognition (HAR) and Speech Recognition are rapidly evolving fields within Data Science, significantly impacting applications in healthcare, security, human-computer interaction, and automation. This paper explores the methodologies, challenges, and advancements in these domains. Machine learning and deep learning models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Transformers play a crucial role in recognizing human activities and speech patterns.