Button icon onto the main Stage. Insert a keyframe for your button at frame 30. The Instance Properties dialog box appears. On the right side, leave the Scene option set to Current Scene and change Frame Number from 1 to 31. Also select the Go To And Play option next to Control at the bottom.
Buttons have many of the same scripting options as keyframes.
Here you should add a Go To command, which lets the user decide when to play the shape tween. Test your movie now and you'll find it starts to replay at the end. You forgot to add a stop action in the final keyframe. To do so, double-click frame 60 of either the Cat or the Dog layer. Go to the Actions tab and add a stop action.