The sequence $a_1$, $a_2$, $a_3$, $\dots$ satisfies $a_1 = 19$, $a_9 = 99$, and, for all $n \ge 3$, $a_n$ is the arithmetic mean of the first $n - 1$ terms. Find the value of $a_2$.

Let's think step by step and output the final answer within \boxed{}.
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