<|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
 A chess tournament is planned for teams, each of which has exactly three players. Each player in a team will play exactly once against each player from all the other teams. For organisational reasons, no more than 250 games can be played in total. Calculate the maximum number of teams that can enter the tournament. 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
7
A chess tournament is planned for teams, each of which has exactly three players. Each player in a team will play exactly once against each player from all the other teams. For organisational reasons, no more than 250 games can be played in total. Calculate the maximum number of teams that can enter the tournament. Express your answer as a single integer.
test