A company has three different sizes of boxes for packaging products: small, medium, and large. The number of products that can fit in each type of box is given by the expressions \(2x\), \(3x\), and \(5x\), respectively, where \(x\) is a positive integer representing a unit of products. The company wants to package a total of \(120\) products. If the number of medium boxes used is at least twice the number of small boxes used and the number of large boxes used is less than three times the number of small boxes used, what is the maximum number of small boxes that can be used? Let's think step by step and output the final answer within \boxed{}.
user