Variable

I would not use True/False variables in this case at all. Variables are useful when you need to carry information/selections/whatever from one slide to another.

Here everything happens within one slide, so you can just use different state when you want the circle to turn grey. If you do that as a disabled state, then you will get the added benefit that the grey circles will not react to hovering if plan to add those info boxes that appear when you hover over active circles. And normal state should be the original color.

Then just add triggers to the buttons so that the blue button sets the states of blue circles to normal and others to disabled and so on. That should get it working, and there is no need for any variables.