Given the parabola equation as $y=a x^{2}+b x+c(a \neq 0)$. Inside it, construct a circle $\odot C_{1}$ with radius $\frac{1}{|a|}$ that is internally tangent to the parabola. Construct $\odot C_{2}$ to be externally tangent to $\odot C_{1}$ and internally tangent to the parabola. Construct $\odot C_{3}$ to be externally tangent to $\odot C_{2}$ and internally tangent to the parabola, and so on, resulting in a sequence of circles $C_{1}, C_{2}, C_{3}, \cdots$, $C_{n}, \cdots$. Find the sum of the areas of the first $n$ circles.