
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
What is the number of centimeters in the length of $GH$ if $AB\parallel CD\parallel EF\parallel GH$?

[asy]
size(6cm,6cm);
pair A,B,C,D,E,F,G,H,X;

A=(0,1);
B=(1,1);
C=(1,0);
X=(0,0);
D=(1/3)*C+(2/3)*X;

draw (A--B--C--D);
draw(D--B);
draw(A--C);

E=(0.6,0.4);
F=(1,0.4);
draw(E--F);

G=(0.7,0.2);
H=(1,0.2);
draw(G--H);

label("$A$",A,NW);
label("$B$",B,NE);
label("$C$",C,SE);
label("$D$",D,SW);
label("$E$",shift(-0.1,0)*E);
label("$F$",F,E);
label("$G$",shift(-0.1,0)*G);
label("$H$",H,E);

label("$120$ cm",midpoint(C--D),S);
label("$180$ cm",midpoint(A--B),N);

[/asy]

Present the answer in LaTex format: \boxed{Your answer}
user