<|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 rectangular prism has three distinct faces of area  $24$ ,  $30$ , and  $32$ . The diagonals of each distinct face of the prism form sides of a triangle. What is the triangle’s area? 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
A rectangular prism has three distinct faces of area  $24$ ,  $30$ , and  $32$ . The diagonals of each distinct face of the prism form sides of a triangle. What is the triangle’s area?
test