<|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
 the total age of a and b is 11 years more than the total age of b and c, while the total age of a and c is 15 years more than the total age of c and d. If the total age of b and d is 36 years, and a's age is the square of d's age, determine the age difference between the oldest and the youngest person among a, b, c, and d, given that all their ages are whole numbers. 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
56
the total age of a and b is 11 years more than the total age of b and c, while the total age of a and c is 15 years more than the total age of c and d. If the total age of b and d is 36 years, and a's age is the square of d's age, determine the age difference between the oldest and the youngest person among a, b, c, and d, given that all their ages are whole numbers.
test