<|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 sum of the squares of three positive numbers is  $160$ . One of the numbers is equal to the sum of the other two. The difference between the smaller two numbers is  $4.$  What is the difference between the cubes of the smaller two numbers?

*Author: Ray Li*

<details><summary>Clarification</summary>The problem should ask for the positive difference.</details> 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
320
The sum of the squares of three positive numbers is  $160$ . One of the numbers is equal to the sum of the other two. The difference between the smaller two numbers is  $4.$  What is the difference between the cubes of the smaller two numbers?

*Author: Ray Li*

<details><summary>Clarification</summary>The problem should ask for the positive difference.</details>
test