Question 13Real numbers $a$ and $b$ are chosen with $1 \lt a \lt b$ such that no triangle with positive area has side lengths $1,$ $a,$ and $b$ or $\tfrac1b,$ $\tfrac1a,$ and $1.$ What is the smallest possible value of $b?$$\dfrac{3+\sqrt{3}}{2}$$\dfrac{5}{2}$$\dfrac{3+\sqrt{5}}{2}$$\dfrac{3+\sqrt{6}}{2}$$3$