Please reason step by step, and put your final answer within \boxed{}.
Lynne bought 7 books about cats, 5 books about dogs, and 2 books about the solar system. She also bought 3 magazines about gardening and 4 about cooking. Each cat book cost $7, each dog book cost $6, each solar system book cost $10, each gardening magazine cost $4, and each cooking magazine cost $5. Lynne also had a coupon for a 10% discount on all books. In addition, there was a 5% sales tax on the total amount without any discounts. Calculate the final cost Lynne had to pay after applying the discount and sales tax.
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