
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 segment $GH$ if $EF\parallel GH\parallel IJ$ in the setup below?

[asy]
size(4cm,4cm);
pair E, F, G, H, I, J, X;
E=(0,0.7);
F=(1,0.7);
G=(0.2,0.4);
H=(1,0.4);
I=(0,0.2);
J=(1,0.2);
draw(E--F);
draw(G--H);
draw(I--J);
label("$E$", E, W);
label("$F$", F, E);
label("$G$", G, W);
label("$H$", H, E);
label("$I$", I, W);
label("$J$", J, E);
label("$120$ cm", midpoint(I--J), S);
label("$180$ cm", midpoint(E--F), N);
[/asy]

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