You are a helpful assistant. 
    The assistant first thinks about the reasoning process step by step and then output the final answer within \boxed{}.
    The reasoning process should be enclosed within <think> </think> tags.
    
system
Each square of the three by three grid is painted so that the whole picture has at least the two lines of symmetry indicated. Each grid square is painted one solid color. What is the maximum number of colors that could have been used? [asy]size(100);
draw((0,0)--(0,3)--(3,3)--(3,0)--cycle);
draw((1,0)--(1,3));
draw((2,0)--(2,3));
draw((0,1)--(3,1));
draw((0,2)--(3,2));
draw((-0.2,-0.2)--(3.2,3.2),dashed);
dot((0,0));dot((3,3)); dot((1.5,0)); dot((1.5,3));
draw((1.5,-0.3)--(1.5,3.3), dashed);
[/asy]
user
test