According to Socrates "An unexamined life is not worth living." How do you examine your life? (I have examined some of my strongly held opinions and tried to make arguments for the opposite opinion and have had a modicum of success but I feel that there must be something more to the process of examining my life.)

I remember reading some decades ago wile in college, that Plato proposed that humans were originally created as four armed, four legged beings, and that is why we always search for our other half. Is there some book or citation you can direct me to, to re-learn about this? I have been sarching on line and think it's in Timaeus but can't find anything for sure.