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Reese, who was in London to premiere her new film Wild, added at the press conference: "I guess maybe we all like to define people by the way the media presents them, and I think that I showed I have a complexity that people didn't know about.
"It's part of human nature. I made a mistake. We all make mistakes. The best you can do is say sorry and learn from it and move on."
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Reese was arrested with her husband Jim Toth for driving under the influence and disorderly conduct.
The Oscar winner attended the premiere at the 2014 BFI London Film Festival wearing a stunning black lace gown and striking make-up.
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Wild is the true story of Cheryl Strayed, a young women who decides to hike the 1,100-mile Pacific Crest trail alone following a devastating personal tragedy. The film is considered a strong award nominee, and could see Reese nab a second Oscar nomination following her win in 2006 for Walk The Line.
During the press conference Reese also discussed filming key scenes in Wild, including how her character's inexperience was easy to replicate.
"When you see me putting together the tent, that's literally me putting together the tent. It took me two hours", she revealed.
She also admitted that she was hoping her rucksack would be full of newspaper, but director Jean-Marc Vallee had other ideas. "I got there on the day, and Jean-Marc said, 'Actually, I think it would be better.' And I said: 'Are you joking?' And he said, 'No, I think it would be better' and then just walked off."
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She continued: "So I ended up carrying it the whole time. I've never been as strong as I was after that movie. I had a back problem."
Wild is out in the UK on 15 January 2015