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The process of incorporating the bevel and emboss effect into Flutter Custom Paint involves the following steps:

1. Create a CustomPainter class that extends from the CustomPainter class in Flutter.

2. Override the paint function of the CustomPainter class to draw the required shape using the provided Canvas object.

3. Within the paint function, create a Paint object with the desired color and style for the shape, and use the Canvas.drawPath method to draw the shape.

4. To add a bevel and emboss effect to the shape, create two additional Paint objects – one for the bevel effect and one for the emboss effect.

5. Use the Canvas.drawShadow method to draw the bevel and emboss effects around the edges of the shape.

6. Set the parameters for the bevel and emboss effects, such as the color, blur radius, and offset.

7. Finally, call the Canvas.clipPath method to clip the shape to its boundary and prevent the bevel and emboss effects from overflowing.

8. Return the completed paint function and use it to create a CustomPaint widget in the app.

9. Use the CustomPaint widget to display the bevel and emboss effect on the required shape in the app.