<|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
 Given an arithmetic sequence {a_n} with the sum of its first n terms denoted as S_n, if points M, N, and P are collinear, and O is the origin, and the vector equation $$\overrightarrow {ON}=a_{15}  \overrightarrow {OM}+a_{6} \overrightarrow {OP}$$ holds (the line MP does not pass through point O), calculate the value of S_{20}. Express your answer as a single integer. 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
10
Given an arithmetic sequence {a_n} with the sum of its first n terms denoted as S_n, if points M, N, and P are collinear, and O is the origin, and the vector equation $$\overrightarrow {ON}=a_{15}  \overrightarrow {OM}+a_{6} \overrightarrow {OP}$$ holds (the line MP does not pass through point O), calculate the value of S_{20}. Express your answer as a single integer.
test