The point $(4 + 7 \sqrt{3}, 7 - 4 \sqrt{3})$ is rotated $60^\circ$ counter-clockwise about the origin.  Find the resulting point.
<|im_start|>system
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<|im_start|>user
The point $(4 + 7 \sqrt{3}, 7 - 4 \sqrt{3})$ is rotated $60^\circ$ counter-clockwise about the origin.  Find the resulting point.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(8,14)
The point $(4 + 7 \sqrt{3}, 7 - 4 \sqrt{3})$ is rotated $60^\circ$ counter-clockwise about the origin.  Find the resulting point.
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