I wish to figure out how the flux of the sun's reflected light from a planet varies with distance, so assume an observer is on the sun, looking at a planet, and the light originating from the planet is just the sun's light being reflected back.

The solar flux a planet receives is inverse squarely proportional to it's distance from the sun, but I get stuck considering how to deal with the reflection.

I originally thought I could consider the planet as a new light source, with luminosity equal to the incident flux times some function of the phase angle, i.e

$L_p = k(\theta)L_{\odot}/d^2$.

In this case, to calculate the flux as seen from the sun we can apply the inverse square law again and obtain

$F = L_p/4\pi d^2 = k(0)L_{\odot}/4\pi d^4.$

But then I considered a thought experiment: if the planets were perfect mirrors, then I'd just be seeing the sun's light but at a distance of $2d$, so the flux I'd see would be inverse squarely proportional to the distance, a different result to the $d^{-4}$ proportionality above.

Where's the flaw(s) in my reasoning?