
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 $P(ka, kb)$, $Q(kb, ka)$, $R(-ka, -kb)$, and $S(-kb, -ka)$, where $a$ and $b$ are consecutive integers with $a > b > 0$ and $k$ is an odd integer, with an area of $50$. Calculate $k(a+b)$.

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