How to find out if coordinate is within shape (.shp file) in python (maybe through pyshp package)?

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I'm trying to map coordinate data to a municipality. Reverse geocoders aren't as accurate as I need them to be, so I found a .shp that maps all the municipalities.

I'm not familiar with .shp files, and was hoping someone familiar with it could help me understand the data it stores and how to read it with pyshp.

What kind of information is stored in a .shp file? Would the municipality names be stored in the file/does anyone have experience using this package that could help me?

Thanks in advance!

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