Let $L$ be the line in space that passes through the origin and the point $(2,1,-2).$  Find the reflection of the point $(3,6,15)$ across $L.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $L$ be the line in space that passes through the origin and the point $(2,1,-2).$  Find the reflection of the point $(3,6,15)$ across $L.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-11,-10,-7)
Let $L$ be the line in space that passes through the origin and the point $(2,1,-2).$  Find the reflection of the point $(3,6,15)$ across $L.$
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