Her 12-year-old daughter Liv marvels at how many famous people she gets to meet

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Julianne Moore is a prolific actress and a knock out beauty.

She’s also a four-time Oscar nominee, a best-selling children’s book author, a humanitarian working with multiple charities and a mother of two children. To most of the world, Moore is highly admired, inspiring and a rad woman. But one person – the Golden Globe winner’s 12-year-old daughter Liv – has recently caught on what an impressive lady her mom really is.

“My kids just see me as Mom. They don’t think of me as being cool,” Moore, 53, told PEOPLE at Saturday’s 7th annual Veuve Clicquot Polo Classic at Liberty State Park in Jersey City, N.J.

But by playing the role of President Alma Coin in the Hunger Games: Mockingjay and costarring with Robert Pattinson in the drama Maps to the Stars – which she was awarded the Best Actress honor at last month’s Cannes Film Festival – has scored some cool mom points.

“She can’t understand that I get to meet all these people she finds so interesting,” Moore said. “She’s like, ‘What is it Mom with you and Chloë Moretz, Kristen Stewart, Robert Pattinson and Jennifer Lawrence?’ She’s baffled by it. She doesn’t understand why it’s happening because I’m just Mom to her. There may have been some moments when she did think I was cool and that’s pretty good!”

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