
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 $GH$ in centimeters if $PQ\parallel RS\parallel GH$?

[asy]
size(4cm,4cm);
pair P,Q,R,S,G,H,X;

P=(0,1);
Q=(1,1);
R=(1,0);
X=(0,0);
S=(1/3)*R+(2/3)*X;

draw (P--Q--R--S);
draw(S--Q);
draw(P--R);

G=(0.6,0.4);
H=(1,0.4);

draw(G--H);

label("$P$",P,NW);
label("$Q$",Q,NE);
label("$R$",R,SE);
label("$S$",S,SW);
label("$G$",shift(-0.1,0)*G);
label("$H$",H,E);

label("$120$ cm",midpoint(R--S),S);
label("$180$ cm",midpoint(P--Q),N);
[/asy]

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