<|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 triangular pyramid \( P-ABC \), given \( BC=3 \), \( CA=4 \), \( AB=5 \). If the dihedral angles between the three lateral faces and the base face are all \( 45^{\circ} \), find the volume of the triangular pyramid \( P-ABC \). 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
2
In the triangular pyramid \( P-ABC \), given \( BC=3 \), \( CA=4 \), \( AB=5 \). If the dihedral angles between the three lateral faces and the base face are all \( 45^{\circ} \), find the volume of the triangular pyramid \( P-ABC \).
test