
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
The interior of a quadrilateral is bounded by the graphs of $(x+by)^2 = 9b^2$ and $(bx-y)^2 = 4b^2$, where $b$ is a positive real number. Determine the area of this region in terms of $b$, valid for all $b > 0$.

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