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The sentence that most likely comes next is: "The final step is to rinse the dog in a manner that preserves one's clothing from being damaged."
Explanation: The previous sentence states that the dog shakes himself and covers you with lather, implying that the dog is already covered in shampoo. Therefore, the next logical step would be to rinse off the shampoo from the dog's coat. This is supported by the sentence mentioning the final step and the need to preserve one's clothing from being damaged during the rinse.