<|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
 In a chess tournament, 30 players participated, each playing exactly one game with every other player. A win was awarded 1 point, a draw 0.5 points, and a loss 0 points. What is the maximum number of players that could have exactly 5 points at the end of the tournament? 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
11
In a chess tournament, 30 players participated, each playing exactly one game with every other player. A win was awarded 1 point, a draw 0.5 points, and a loss 0 points. What is the maximum number of players that could have exactly 5 points at the end of the tournament?
test