White background vs Shadow and Mirror

Hi All, please help.

look at the picture attached (example.jpg). The box casts shadow on a plane and also reflects in it (mirror). I made the shadow red just emphasize I need to have it red.

What I want to achieve is to make the plane invisible - so there’s no gray gradient. In short: box, shadow, reflection and nothing else but the white background. How to achieve that?

There’s one ALMOST good solution: make the plane “shadow only” and “ztransp” (it won’t reflect the box), create another plane for reflection and make it “shadeless”. This solution works (attachment: example2.jpg). There’s a drawback however - when you make a plane “shadow only” the shadow color stops working (it’s always black) - example2.jpg.

Thank you,