More recently, several attempts have been made to simultaneously design desired functional molecules and their synthetic routes under a unified methodological framework. For a given reaction prediction model, a virtual library of candidate molecules can be created by which a set of reactants is given to the model to produce its synthetic product. In addition, the properties or a certain score of a candidate molecule can be calculated using machine learning models or an arbitrary reward function. By obtaining the inverse mapping of such a cascade model, which defines the composite mapping from any given reactant set to a product and from the product to its physicochemical properties, the products exhibiting desired properties and their reactant sets can be predicted simultaneously. The Molecule Chef algorithm proposed by uses a cascaded forward model that connects a deep generative model of reactant molecules for the reaction prediction , and a property prediction model for the created virtual products. Gottipati et al. formulated the inverse problem of such a cascade model as a combinatorial optimization problem over a set of commercially available compounds, and proposed a reinforcement learning algorithm to identify the promising combination of reactant molecules. However, there are still many unsolved technical problems in these existing methods. In addition, their predictive performance and systematic evaluation from the viewpoint of organic chemistry are insufficient, and they have not yet reached the level required for practical adoption.