
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
Let \( A B C D \) be a parallelogram with \( A B = 8 \), \( A D = 11 \), and \( \angle B A D = 60^{\circ} \). Let \( X \) be on segment \( C D \) with \( \frac{C X}{X D} = \frac{1}{3} \) and \( Y \) be on segment \( A D \) with \( \frac{A Y}{Y D} = \frac{1}{2} \). Let \( Z \) be on segment \( A B \) such that \( A X \), \( B Y \), and \( D Z \) are concurrent. Determine the area of triangle \( X Y Z \).

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