
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
Triangle $XYZ$ has an altitude from point $X$ to side $YZ$, measuring 9 cm, with $YZ = 15 \text{ cm}$. A rectangle $ABCD$ is inscribed in triangle $XYZ$ such that side $AD$ of the rectangle lies along side $YZ$ of the triangle. The length of segment $AB$ is one-third the length of segment $AD$. Determine the area of rectangle $ABCD$.

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