Understanding Acceleration on a Moving Incline

[premitive1]

"a block of mass m is sliding on a frictionless incline of 30 degrees. this incline has mass m and it has no friction with the ground. compute the acceleration for both objects."

I'm having some conceptual trouble with this problem as it's been a while since my physics course and I've had little practice since.

as the block slides down the incline the incline will begin moving along the horizontal axis.
supposing the block and incline are on the left, the motion of the incline will be in the positive x direction.

this is what I've tried so far

the force on the incline in the x direction will be the force of the box on the surface of the incline times cos 60 degrees. there is no net force in the y direction on the incline.

supposing I understood the above correctly, I'm at a loss concerning where to go next.
forces acting on the box relative to the incline include gravity and a normal force perpendicular to the incline. the force acting in the x direction on the box is then only the x component of the normal force.
is the acceleration of the box in the x direction the result of the x component of the normal force and the acceleration of the incline in the positive y direction?
and its acceleration in the y direction the result of gravity and the y component of the normal force?

I think that's the idea, what may have been confusing me before is that I was including a force acting on the box perpendicular to the surface causing the normal force, but I think now that the normal force only reacts to the component of gravity in the direction of the incline?
a worked out solution would be great, and any comments on my confusions also appreciated

 

[premitive1]

also, I've looked through similar questions asked on the forum and none of them are quite similar to this, although I think they have helped me conceptualize the situation a bit better.

 

[ashishsinghal]

the force on the incline in the x direction will be the force of the box on the surface of the incline times cos 60 degrees. there is no net force in the y direction on the incline.

This is correct!

forces acting on the box relative to the incline include gravity and a normal force perpendicular to the incline. the force acting in the x direction on the box is then only the x component of the normal force.

That is also correct!

is the acceleration of the box in the x direction the result of the x component of the normal force and the acceleration of the incline in the positive y direction?

Why would that be? Please make this line more clear. Show the logic behind it.

its acceleration in the y direction the result of gravity and the y component of the normal force?

This is correct!

I think that's the idea, what may have been confusing me before is that I was including a force acting on the box perpendicular to the surface causing the normal force, but I think now that the normal force only reacts to the component of gravity in the direction of the incline?

This is not correct. Please make yourself more clear and attach an FBD.