The 42nd question: Given infinite real sequences $a_{1}, a_{2}, \ldots$ and $b_{1}, b_{2}, \ldots$, for $n \geq 1$, we have $a_{n+1}+b_{n+1}=\frac{a_{n}+b_{n}}{2}$, $a_{n+1} b_{n+1}=\sqrt{a_{n} b_{n}}$. Suppose $b_{2016}=1$ and $a_{1}>0$, find all possible values of $a_{1}$.

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The 42nd question: Given infinite real sequences \(a_{1}, a_{2}, \ldots\) and \(b_{1}, b_{2}, \ldots\), for \(n \geq 1\), we have \(a_{n+1} + b_{n+1} = \frac{a_{n} + b_{n}}{2}\) and \(a_{n+1} b_{n+1} = \sqrt{a_{n} b_{n}}\). Suppose \(b_{2016} = 1\) and \(a_{1} > 0\), find all possible values of \(a_{1}\).