(CBS News) NEW YORK -- South Korean President Park Geun-hye is a fascinating character -- she's the first woman president in a male-dominated society, and she's as tough as they come. Her father was President of South Korea for more than twenty years before he was assassinated; her mother was also assassinated, and Park herself was viciously slashed with a razor in 2006.
Park will meet with President Obama on Tuesday, but first she spoke to CBS News in her first television interview.
The last time North Korea attacked the South was three years ago -- it shelled an island, killing four people. South Korea's military did not return fire. We asked South Korea's new president how she would respond.
MARGARET BRENNAN: Would a small-scale attack like what happened in 2010 be considered a provocation worthy of a military response by you?
PRESIDENT PARK: Yes, we will make them pay.
Since becoming president, Park Geun-hye has taken a hardline approach to North Korea. In the past, a weapons test was followed by negotiations to exchange food aid and money for North Korea to halt its nuclear program.
Park says she won't play that game.
"So North Korea engages in provocations, threats, this is followed by negotiations and assistance, and so we saw an endless continuation of this vicious cycle, and it is time for us to put an end to the cycle," she says.
North Korea's rhetoric has not helped. Last month, its state media used a traditional term for a woman who has forgotten her place.
BRENNAN: The North said that the venomous swish of your skirt was responsible for the build-up in tensions -- what did that mean to you? How did that make you feel?
Watch the entire interview at left
PRESIDENT PARK: In my view, the very fact that they're not basing their comments on facts, but resorting to various ad hominem attacks, referring to my dress and whatnot, is a sign that they have very weak rationale -- that their rationale is extremely weak and they feel cornered. I think it's a telling sign of that.
Park brushed off the verbal attack -- her toughness has earned her the nickname the Iron Lady of Asia.
Even though her mother was killed by a North Korean spy, she still met face-to-face in 2002 with the man who likely ordered that attack: North Korea's Kim Jong Il, the father of the current president.
BRENNAN: Would you meet with Kim Jong Un face to face, and what would you say?
PRESIDENT PARK: I would tell him that North Korea must change. That is the only way for survival and the only way to development.
President Park and President Obama are scheduled to meet at the White House Tuesday. U.S. officials want to know whether Park thinks it's possible to begin talks with North Korea about its nuclear program. She told CBS News that if North Korea takes the right steps, they will be rewarded. So far, she has not received the response she hoped for and she said the United States, China and other world powers need to put them in a situation, force them to change, and give them no choice. That's an even harder line policy.