A farmer needs to buy bags of feed for his livestock. Each bag of feed can support 5 animals for a week. The farmer has a total of 30 animals. He wants to ensure he has enough feed for at least 4 weeks, but he can only buy up to 35 bags of feed due to budget constraints. What is the minimum number of bags of feed he needs to buy to support all his animals for 4 weeks, and does he stay within his budget constraints? Let's think step by step and output the final answer within \boxed{}.
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