i’ve been where you are with the specs (my device was an Acer Aspire with 6GB of RAM, iGPU, and a Duo Core i3). Some of the best games i got to run on there were Emulated Games. Assuming that’s off the table though:

• Alan Wake is a decently low speced game and i highly recommend if you want Action and Story Rich (the original one from 2010, not the remaster).
• Fallout 3 & New Vegas. I got them to run pretty well out of the box and both i can say meet the Action criteria.
• If you want an online game Team Fortress 2 runs on anything really made in the last 10 years assuming you get your settings right.
• Continuing with the Valve Train, Portal 1, Portal 2, and Half Life 1 all run pretty well. All 3 can be pretty high action at times (Half Life more so than portal)
• Project Zomboid as far as i know is also pretty low spec. It’s a survival game which can be really high action depending on how you play it (you can customize the spawn settings however you like). Story Rich though? It leaves a lot to be desired in that department.
• Max Payne is old, but it’s really high action and has a phenomenal story.