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What tool should I use to select or identify geographic units that are adjacent to the U.S. coastline feature in ArcMap?

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The Census cartographic boundary shapefiles do not include offshore areas. You could use a Select by Location to look for tracts which intersect the cartographic boundaries. You'll need to account for tracts bounding Canada and Mexico; a few sources for administrative boundary files, such as gadm.org, are listed in Seeking administrative boundaries for various countries?

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