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The 6-foot-2, 215-pound Garcia is a career .257 hitter in seven Minor League seasons and has been praised by prospect publications for his throwing arm.
Coats hit .200 in 28 games with the White Sox, spending the majority of the season at Triple-A Charlotte. The 26-year-old hit .330 with 22 doubles and 10 home runs in 78 Minor League games.
The White Sox 40-man roster remains full.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.