What is the greatest three-digit number "abc'' such that $4,a,b$ forms a geometric sequence and $b,c,5$ forms an arithmetic sequence?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the greatest three-digit number "abc'' such that $4,a,b$ forms a geometric sequence and $b,c,5$ forms an arithmetic sequence?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
697
What is the greatest three-digit number "abc'' such that $4,a,b$ forms a geometric sequence and $b,c,5$ forms an arithmetic sequence?
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