
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 \(ABCD\), the lengths of the bases \(AD = 24 \text{ cm}\), \(BC = 8 \text{ cm}\), and the diagonals \(AC = 13 \text{ cm}\), \(BD = 5\sqrt{17} \text{ cm}\) are known. Calculate the area of the trapezoid.

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