<s>[INST] A peace advocacy group is planning to hold a large outdoor rally in Cairo. They wish to rent a stage with a floor area of at least $1,600$ square meters. However, because of the surroundings of the rally site, they must constrain the dimensions ($x$ and $y$) of the stage to be greater than $10$ meters and the sum of the dimensions to be less than $50$ meters. What are the minimum dimensions for the stage that satisfy all the given conditions?[/INST]