
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
In the trapezoid shown, the ratio of the area of triangle $ABC$ to the area of triangle $ADC$ is $8:2$. If the total length of $AB + CD = 150$ cm, and the segment $\overline{AB}$ is three times the length of segment $\overline{CD}$, how long is segment $\overline{AB}$? [asy]
import olympiad; size(150); defaultpen(linewidth(0.8));
pair A = (0,0), B = (8,0), C = (5,2), D = (2,2);
draw(A--B--C--D--cycle--C);
label("$A$",A,SW); label("$B$",B,SE); label("$C$",C,NE); label("$D$",D,NW);
[/asy]

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