Carole Black's beauty role model? Tina Turner. "She's age-defying," says the Cincinnati native. Black is burnin' along pretty well herself. The energetic 57-year-old, who divides her time between a two-bedroom apartment in Manhattan and a house in Beverly Hills, is the CEO and president of Lifetime TV, the female-oriented channel that she has built into basic cable's No. 1 network since taking the helm in '99. Divorced and the mother of a grown son, Black was raised by her Armenian grandparents after her parents split up when she was a baby. Her grandmother, she says, "made me feel I could do everything in life." Annie Potts, who stars in the Lifetime drama Any Day Now
, sees the results. "Carole's very smart about what she does," says Potts, "and it seems like it's effortless." But the 5'3½" Black admits to doing a few dumb things for beauty. There was the time she tweezed her eyebrows too thin "and looked surprised for about six months," she says. "And when I was about 25, I saw an ad for these pants that you attach to a vacuum cleaner to suck off weight. All they did was make me perspire. What was I thinking?"