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Puzzle Monster Presents: Chained Melodies Unravel the titles of famous songs! Only $1.99!

Ann Mary Weird, Absurdist Lyricist, is really just a plagiarist. She took the first verses of two songs by one well-known band and split them into chunks of three, four or five words. Then she selected fragments, alternating between the two original verses, until she compiled a "new" verse. Can you identify the original songs and the original classic rock band - without resorting to a search engine?