A gas is contained in a cylinder with a movable piston. Initially, the gas occupies a volume of 4 liters at a pressure of 3 atmospheres and a temperature of 300 Kelvin. The gas then undergoes a transformation where its volume is doubled, and its temperature is increased to 450 Kelvin. What is the new pressure of the gas? Let's think step by step and output the final answer within \boxed{}.
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