<|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
 There are several children. The first child has 2 more candies than the second child, the second child has 2 more candies than the third child, and so on, with each preceding child always having 2 more candies than the following child. They sit in a circle and play a game. Starting with the first child, they give 2 candies to the next child, the second child gives 4 candies to the third child, and so on, with each child always adding their 2 candies to the ones received from the previous child before passing them on. During the game, at some point, a child receives candies from the previous child but is unable to pass them on as per the rules, and at this point, the ratio of candies between two neighboring children is $13 : 1$. What is the maximum number of children? 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
25
There are several children. The first child has 2 more candies than the second child, the second child has 2 more candies than the third child, and so on, with each preceding child always having 2 more candies than the following child. They sit in a circle and play a game. Starting with the first child, they give 2 candies to the next child, the second child gives 4 candies to the third child, and so on, with each child always adding their 2 candies to the ones received from the previous child before passing them on. During the game, at some point, a child receives candies from the previous child but is unable to pass them on as per the rules, and at this point, the ratio of candies between two neighboring children is $13 : 1$. What is the maximum number of children?
test