Color challenged

Remember this picture from my first photo reveal of the new house? This will be our main livings pace. This picture, from the RMLS, is taken from the dining room looking into the living room. The carpet in this room is posing a BIG color challenge for me.

Not only is a color I would never choose but feels like the dominant color due to its mass. Furthermore it clashes with almost all of the colors/accessories in our previous home which had a lot of bright red, orange and yellow throughout.

While we still don't have keys yet we know that one of our first projects will be painting, painting and more painting. Because every interior wall in this house needs repainted badly I want to start wrapping my head around an overall color pallet for the house and have some paint chips ready to put up right away. We know we want to paint Margot's room a soft grey. But unlike a lot of empty houses which serve as a blank slate this one comes with a lot of color already. Besides the rose carpet and two wood tones throughout the house there is the green marble fireplace, brick red/brown tile in the kitchen, pink and maroon tile and fixtures in Margot's bathroom and pink and grey marble in the master bath. And that's just the first floor. The lower level has it's own wacky color palate that is a topic for another day.

My instinct is that with so many colors already in play the walls should be light and neutral. But what neutral? Should we stick tot he off white/ivory currently in the house? What about adding a different shade of grey throughout the main space? Grey and pink is a pretty classic 1950's color combination. But how might grey and pink work with our existing furniture especially the yellow/gold/ivory chairs?

Unfortunately the pink carpet is here to stay (at least for the next several years) as is all the pink/brown/maroon tile. Given that, the challenge is to make it not only work for now but look good in the meantime. Ideas? Brilliant neutral paint colors to share? Ginormous inexpensive area rug ideas to tone down the endless pink?