Another important “tool” kids (and adults) need is the knowledge that “others matter” and the ability to act accordingly. I think this starts quite young when kids learn to share and to consider others in addition to themselves.
If this could be inculcated in everyone I think it would go a long way to preventing violence and/or limiting its severity. It seems to me that the lack of the realization that “others matter” is often at the root of violent action. It is more difficult to act violently toward another if you think of them as someone with worth, someone you might share something with. It is much easier to be violent toward someone you see strictly as “them”, particularly as a “them” divorced from your experience and with no personal worth or value.
This “others matter” most often needs to be a personal social experience, but can be generalized to more “others” from even limited experience. It is not something that can be acquired vicariously over the Internet or through some other media source, unless preset with some experience of “others”. For this we need some personal experience, we need to teach kids (and have them experience) how to act with others, that others matter and that it is good to share.