How to group points based of user-provided distance in ArcGIS

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I have a point layer and I need to group/aggregate the points within a 1km proximity into 1 single point to create a new point layer.

I was trying to use Aggregate point and then Feature to point, but it eliminates the single points I have in case there are no other points in 1km proximity, but I need to be able to save those single points too. It also groups only three or more points.

Any help you can offer would be appreciated!



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