CMIMC 2023 Team Problem 4

Suppose a_{1}, a_{2}, a_{3}, \ldots, is a sequence of real numbers such that

a_{n}=\frac{a_{n-1} a_{n-2}}{3 a_{n-2}-2 a_{n-1}}

for all n \geq 3. If a_{1}=1 and a_{10}=10, what is a_{19}?