7
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The side lengths of both triangles to the right are given in centimeters. What is the length of segment $AB$?

[asy]
pair A,B,C,D,E,F,G;

A=(0,0);
B=12*dir(0);
C=20*dir(120);
D=8+B;
E=D+6*dir(0);
F=D+10*dir(120);

draw(A--B--C--cycle);
draw(D--E--F--cycle);

label("A",F,N);
label("B",E+(1.4,0));
label("6",.5*(A+B),S);
label("14",.5*(B+C),NE);
label("10",.5*(A+C),SW);
label("\small{$120^{\circ}$}",A,NE);
label("3",.5*(D+E),S);
label("5",.5*(D+F),SW);
label("\tiny{$120^{\circ}$}",D+(1.8,0.8));

[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7
The side lengths of both triangles to the right are given in centimeters. What is the length of segment $AB$?

[asy]
pair A,B,C,D,E,F,G;

A=(0,0);
B=12*dir(0);
C=20*dir(120);
D=8+B;
E=D+6*dir(0);
F=D+10*dir(120);

draw(A--B--C--cycle);
draw(D--E--F--cycle);

label("A",F,N);
label("B",E+(1.4,0));
label("6",.5*(A+B),S);
label("14",.5*(B+C),NE);
label("10",.5*(A+C),SW);
label("\small{$120^{\circ}$}",A,NE);
label("3",.5*(D+E),S);
label("5",.5*(D+F),SW);
label("\tiny{$120^{\circ}$}",D+(1.8,0.8));

[/asy]
train