Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.

Four positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine the smallest possible value of $d$ such that the arithmetic mean of the numbers $a, b, c$ is half of the arithmetic mean of the numbers $a, b, c, d$.

Remember to put your answer on its own line after "Answer:".
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