
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 \(5:3\). If \(AB + CD = 160\) cm, how long is segment \(\overline{AB}\)? Assume the same configuration for the vertices \(A, B, C, D\) as in the original problem.

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