When they talk about an inventory how much detail do they need. All it says in the scope. Does this mean all workstations, and peripherals like monitors, printers etc? Or is it as simple as all routers, switches, firewalls etc.
Having a complete asset list is always beneficial anyway as a company.
We use Lansweeper to do this to show all the network connected devices and their current status. Quite inexpensive, but also gives masses of support information on the devices such as configs, errors logs, patch levels, etc.