<|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
 In the given figure, \(ABCD\) is a rectangle and triangles \(\triangle ABE\) and \(\triangle CDF\) are right triangles. The area of triangle \(\triangle ABE\) is \(150 \mathrm{~cm}^{2}\) and the lengths of segments \(AE\) and \(DF\) are 15 cm and 24 cm, respectively. What is the length of segment \(CF\)? 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
In the given figure, \(ABCD\) is a rectangle and triangles \(\triangle ABE\) and \(\triangle CDF\) are right triangles. The area of triangle \(\triangle ABE\) is \(150 \mathrm{~cm}^{2}\) and the lengths of segments \(AE\) and \(DF\) are 15 cm and 24 cm, respectively. What is the length of segment \(CF\)?
test