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Most object manipulation strategies for robots are based on the assumption that the object is rigid (i.e., with fixed geometry) and the goal's details have been fully specified (e.g., the exact target pose). However, there are many tasks that involve spatial relations in human environments where these conditions may be hard to satisfy, e.g., bending and placing a cable inside an unknown container. To develop advanced robotic manipulation capabilities in unstructured environments that avoid these assumptions, we propose a novel long-horizon framework that exploits contrastive planning in finding promising collaborative actions. Using simulation data collected by random actions, we learn an embedding model in a contrastive manner that encodes the spatio-temporal information from successful experiences, which facilitates the subgoal planning through clustering in the latent space. Based on the keypoint correspondence-based action parameterization, we design a leader-follower control scheme for the collaboration between dual arms. All models of our policy are automatically trained in simulation and can be directly transferred to real-world environments. To validate the proposed framework, we conduct a detailed experimental study on a complex scenario subject to environmental and reachability constraints in both simulation and real environments.