
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 quadrilateral has vertices \(P(a, b)\), \(Q(a, -b)\), \(R(-a, -b)\), and \(S(-a, b)\) where \(a\) and \(b\) are positive integers such that \(a > b\). If the area of the quadrilateral \(PQRS\) is \(32\), calculate the value of \(a + b\).

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