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A solo Taylor Swift was spotted strolling in Hollywood yesterday, but the country star has someone on her mind -- that would be TRON hottie Garrett Hedlund!

Swift and Hedlund went on a date in Nashville, Tennessee on April 1, and a source tells Us Magazine, "It was their first time going out. They've been emailing for a while, and she hinted they should get together ... She has actually spent time getting to know Garrett. He's cute -- and he's into country music! [She] likes that he's a normal guy." Hedlund has been in Nashville recording a CD, and Taylor has been traveling from city to city ahead of the US leg of her Speak Now tour, which resumes on May 27.

The duo met up around 8pm and Hedlund was back at his hotel by 12:30am, and after her breakup with Jake Gyllenhaal last fall, it looks like Swift is taking it slow. Back in February, she went on a date with Glee hottie Chord Overstreet, and she previously dated Joe Jonas and Taylor Lautner.