ITAMS stands for IT Asset Management System (creative, right?)
I led a team of 3 developers, myself included.
My team's process was actually very simple. We met with stakeholders to gain visibility into the problem at hand. Each school (6 entities in total) had their own decentralized process for tracking IT assets (or in one case, no process at all). There was no way to know if a computer had an encrypted hard drive or not, where the asset was physically located, who was responsible for it, or what it's disposition was (or would be). There was obviously a lot more to what was needed, but that's the high level.
One thing that I did not want to do (as much as was possible) was just "gather requirements". I have found this to be counter-productive in so many ways. Instead, the approach I took with my team and stakeholders was to really dig into the problem, and get to the root cause. From there my team and I were able to devise a strategy that addressed the underlying issues, which made everyone happy.
We delivered a proof of concept in under a month (one 3-week sprint), and had functional prototypes to users very quickly. Our first releasable product came in just 3 months after the initial planning meeting. We utilized Agile methodologies to get the product to a "1.0" version quickly, and then released new versions at the end of each sprint.