A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: For triangle with vertices A=(9, 4), B=(7, 5), and C=(10, 10), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.
Assistant: Let me solve this step by step.
<think>
user