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R for GIS – calculating proximal densities

I recently started using R for GIS applications and need assistance with calculating proximal densities, a concept I am mostly unfamiliar with. To illustrate, suppose I am provided with schools and playgrounds location data (sample data here) for which I would like to calculate proximal densities at 0.25-mile, 0.50-mile, 0.75-mile, and 1-mile radii. How can this be achieved using R program? I currently do not have much idea about how to approach this and hence, have not included any of my R code.