
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 $P(a+1,b-1)$, $Q(b+1,a-1)$, $R(-a-1, -b+1)$, and $S(-b-1, -a+1)$, where $a$ and $b$ are integers with $a>b>0$. The area of $PQRS$ is $24$. Calculate the value of $a+b$.

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