
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
Given a quadrilateral with vertices $P(k,a)$, $Q(a,k)$, $R(-k,-a)$, and $S(-a,-k)$, where $k$, $a$, and $b$ are integers with $k > a > 0$, find the value of $k+a$, given that the area of the quadrilateral $PQRS$ is $32$.

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