Let $C_1$ and $C_2$ be two concentric reflective hollow metal spheres of radius $R$ and $R\sqrt3$ respectively. From a point $P$ on the surface of $C_2$, a ray of light is emitted inward at $30^o$ from the radial direction. The ray eventually returns to $P$. How many total reflections off of $C_1$ and $C_2$ does it take?

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