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Count points that intersect polylines

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I'm an ArcGIS newbie so please bear with me. I have a shapefile of bike lanes in a particular city (polylines). I have another shapefile with bike accidents in that same city (points). This seems like it should be simple, but I can't figure out how to get a count of how many of those accident points are intersected by (or in other words, lie on top of) a bike lane polyline. As well, in the bike lane attribute table there is a field for bike lane type (route, lane, path) and I'd like to break down the count by those types (ie see separately how many accidents intersect with a bike route, with a bike lane, etc). If that complicates things then I can just create a different shape file for each type, and run the counts separately. My main question is: how do I get a count of the number of points that are intersected by polylines? I've tried using the 'Tabulate Intersection' tool but all my returns have been empty. Any help would be appreciated!

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