
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 $PQRS$ is inscribed in triangle $XYZ$, with side $PS$ of the rectangle on side $XZ$. Triangle $XYZ$ has an altitude from $Y$ to side $XZ$ of 8 inches, and the side $XZ$ measures 15 inches. The length of segment $PQ$ is one-third the length of segment $PS$. Calculate the area of rectangle $PQRS$, and express your answer as a common fraction.

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