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The combination of collaborative robots and end-to-end AI, promises flexible automation of human tasks in factories and warehouses. However, such promise seems a few breakthroughs away. In the meantime, humans and cobots will collaborate helping each other. For these collaborations to be effective and safe, robots need to model, predict and exploit human's intents for responsive decision making processes. Approximate Bayesian Computation (ABC) is an analysis-by-synthesis approach to perform probabilistic predictions upon uncertain quantities. ABC includes priors conveniently, leverages sampling algorithms for inference and is flexible to benefit from complex models, e.g. via simulators. However, ABC is known to be computationally too intensive to run at interactive frame rates required for effective human-robot collaboration tasks. In this paper, we formulate human reaching intent prediction as an ABC problem and describe two key performance innovations which allow computations at interactive rates. Our real-world experiments with a collaborative robot set-up, demonstrate the viability of our proposed approach. Experimental evaluations convey the advantages and value of human intent prediction for packing cooperative tasks. Qualitative results show how anticipating human's reaching intent improves human-robot collaboration without compromising safety. Quantitative task fluency metrics confirm the qualitative claims.