
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
A square \(PQRS\) has a segment \(PT\) that is perpendicular to segment \(TR\), forming a right triangle within the square. If \(PT = 12\) units and \(TR = 9\) units, find the area of pentagon \(PTRSQ\) in square units.

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