
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 $PQ$ in centimeters if $XY \parallel MN \parallel PQ$?

[asy]
size(4cm,4cm);
pair X,Y,M,N,P,Q,Z;

X=(0,2);
Y=(2,2);
M=(2,1);
Z=(0,1);
N=(0.8)*M+(0.2)*Z;

draw (X--Y--M--N);
draw(N--Y);
draw(X--M);

P=(1.2,0.6);
Q=(2,0.6);

draw(P--Q);

label("$X$",X,NW);
label("$Y$",Y,NE);
label("$M$",M,SE);
label("$N$",N,SW);
label("$P$",shift(-0.1,0)*P);
label("$Q$",Q,E);

label("$80$ cm",midpoint(M--N),S);
label("$120$ cm",midpoint(X--Y),N);
[/asy]

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