Yeah, as others mentioned, what you have is a DOCSIS modem, which won't work with FiOS. If you don't have FiOS TV, but know where your ONT is located, consider asking Verizon to switch your Internet connection from Coax to Ethernet, and then connect your own router to the ONT using a CAT5e or better cable.
If you still want to use Coax for your WAN connection supply, take note that the maximum speed is 100Mbps off of that, while Verizon's minimum speed tier today is 200Mbps. You can probably score a used G1100 router as suggested above to upgrade your old ActionTec router if your aim is better Wi-Fi. But long term, I would still get switched over to Ethernet, so you can use your own router and get higher speeds in the future.