<|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
 We have created a convex polyhedron using pentagons and hexagons where three faces meet at each vertex. Each pentagon shares its edges with 5 hexagons, and each hexagon shares its edges with 3 pentagons. How many faces does the polyhedron have? 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
32
We have created a convex polyhedron using pentagons and hexagons where three faces meet at each vertex. Each pentagon shares its edges with 5 hexagons, and each hexagon shares its edges with 3 pentagons. How many faces does the polyhedron have?
test