I'll admit, I added one to the list I've posted here many times.
Full, 100% background check on all sales (require every jurisdiction in the country to accurately maintain their entries)
Require gun handling, firing, safety and storage training, to include all forms of pistols, rifles and shotguns.
Require licensing, want a gun, get a license prior to buying (along with the training).
Register every firearm and accessory. You can do it at the time of the background check.
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Ban high capacity magazines. Outside of combat, no one needs more than 7-8 rounds for a pistol, 10 for a rifle. If you can't kill what you're firing at in that amount of rounds, you shouldn't be carrying a firearm.
As for assault weapons, put an additional tax on any semi-automatic, center fire rifle similar to the tax on full autos. But don't ban them.
I do have some other thoughts, but this list would suffice for now. And no, I wouldn't target mass shootings, just keeping fire arms out of the hands of people who shouldn't have them.