How can I automate reordering pages in several hundred pdf files?

Hi, I'm new to Acrobat.  I've volunteered to help out my local city govt.  They have a lot of pdf files with pages in the opposite order than the need.  I know I can open each one and reorder each page manually, but that could take several months.  I thought perhaps I could write a script or bat file to speed this up.  I was thinking of extracting each page to a working directory and then combining them (in the new sequence) to make a new pdf file.  So far, it doesn't look like there are command line options to allow me to do this.  Has anybody done something like this?  Is it even possible?  Any suggestions greatly appreciated.

Thanks!!!