What is the largest negative integer $x$ satisfying $$24x \equiv 15 \pmod{1199}~?$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the largest negative integer $x$ satisfying $$24x \equiv 15 \pmod{1199}~?$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-449
What is the largest negative integer $x$ satisfying $$24x \equiv 15 \pmod{1199}~?$$
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