<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Let point O be located inside a regular tetrahedron ABCD, and let G be the centroid of the tetrahedron. The line OG intersects each face of the tetrahedron at points A1, B1, C1, and D1. Find the value of the sum of the ratios of A1O to A1G, B1O to B1G, C1O to C1G, and D1O to D1G. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
4
Let point O be located inside a regular tetrahedron ABCD, and let G be the centroid of the tetrahedron. The line OG intersects each face of the tetrahedron at points A1, B1, C1, and D1. Find the value of the sum of the ratios of A1O to A1G, B1O to B1G, C1O to C1G, and D1O to D1G.
test