A factory produces gadgets at a constant rate of 60 gadgets per hour. During an 8-hour shift, the factory must meet a quota of producing at least 500 gadgets. If the factory has already produced 360 gadgets in the first 6 hours, what is the minimum rate (in gadgets per hour) at which the factory needs to produce gadgets for the remaining 2 hours to meet the quota? Let's think step by step and output the final answer within \boxed{}.
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