<|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
 Joey has 30 thin sticks, each stick has a length that is an integer from 1 cm to 30 cm. Joey first places three sticks on the table with lengths of 3 cm, 7 cm, and 15 cm, and then selects a fourth stick such that it, along with the first three sticks, forms a convex quadrilateral. Calculate the number of different ways Joey can make this selection. 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
17
Joey has 30 thin sticks, each stick has a length that is an integer from 1 cm to 30 cm. Joey first places three sticks on the table with lengths of 3 cm, 7 cm, and 15 cm, and then selects a fourth stick such that it, along with the first three sticks, forms a convex quadrilateral. Calculate the number of different ways Joey can make this selection.
test