Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy]
size(140);
void spinner(picture pic=currentpicture, real rotate, int a, int b, int c)
{
dot(pic,(0,0),linewidth(4));
draw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate));
label(pic, "$"+string(a)+"$",dir(30+rotate)/2,fontsize(10pt));
label(pic, "$"+string(b)+"$",dir(150+rotate)/2,fontsize(10pt));
label(pic, "$"+string(c)+"$",dir(-90+rotate)/2,fontsize(10pt));
}
picture p;
spinner(0,-1,-3,5); spinner(p,180,2,4,-6);
draw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy]
size(140);
void spinner(picture pic=currentpicture, real rotate, int a, int b, int c)
{
dot(pic,(0,0),linewidth(4));
draw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate));
label(pic, "$"+string(a)+"$",dir(30+rotate)/2,fontsize(10pt));
label(pic, "$"+string(b)+"$",dir(150+rotate)/2,fontsize(10pt));
label(pic, "$"+string(c)+"$",dir(-90+rotate)/2,fontsize(10pt));
}
picture p;
spinner(0,-1,-3,5); spinner(p,180,2,4,-6);
draw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{5}{9}
Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy]
size(140);
void spinner(picture pic=currentpicture, real rotate, int a, int b, int c)
{
dot(pic,(0,0),linewidth(4));
draw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate));
label(pic, "$"+string(a)+"$",dir(30+rotate)/2,fontsize(10pt));
label(pic, "$"+string(b)+"$",dir(150+rotate)/2,fontsize(10pt));
label(pic, "$"+string(c)+"$",dir(-90+rotate)/2,fontsize(10pt));
}
picture p;
spinner(0,-1,-3,5); spinner(p,180,2,4,-6);
draw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]
train