
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 length of segment $GH$ if $JK \parallel LM \parallel GH$?

[asy]
size(4cm,4cm);
pair J,K,L,M,G,H,Y;

J=(0,1.2);
K=(1.2,1.2);
L=(1.2,0);
Y=(0,0);
M=(1/3)*L+(2/3)*Y;

draw (J--K--L--M);
draw(M--K);
draw(J--L);

G=(0.7,0.5);
H=(1.2,0.5);

draw(G--H);

label("$J$",J,NW);
label("$K$",K,NE);
label("$L$",L,SE);
label("$M$",M,SW);
label("$G$",shift(-0.1,0)*G);
label("$H$",H,E);

label("$120$ cm",midpoint(L--M),S);
label("$180$ cm",midpoint(J--K),N);
[/asy]

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