
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 $JK$ in centimeters if $LM \parallel NO \parallel JK$?

[asy]
size(4cm,4cm);
pair L,M,N,O,J,K,X;

L=(0,1);
M=(2,1);
N=(2,0);
X=(0,0);
O=(0.6)*N+(0.4)*X;

draw (L--M--N--O);
draw(O--M);
draw(L--N);

J=(1.2,0.5);
K=(2,0.5);

draw(J--K);

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

label("$120$ cm",midpoint(N--O),S);
label("$180$ cm",midpoint(L--M),N);

[/asy]

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