Logging or Tracking While Logged Into a Private Area

We are using the Membership plugin to create a member only page of our site. This page has several links to files for them to use. Product and server info, etc.

I would like to be able to create a report that shows when the user logs into the site and what links they click on. In particular, the links within the secured page(s).

The purpose of this is to know who is logging in, how often and what they are downloading.

Is there a way to do this with Membership? If not, what would it take to modify it for this purpose?