
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
Rectangle $ABCD$ is inscribed in triangle $PQR$ such that side $AD$ of the rectangle is on side $PR$ of the triangle. The triangle's altitude from $Q$ to side $PR$ is 9 inches, and $PR = 15 \text{ inches}$. 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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