
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
Four of the vertices of a rectangle are located at $(4, 9)$, $(15, 9)$, $(15, -4)$, and $(4, -4)$. Determine the area of the intersection between this rectangle and the region inside the graph of the equation $(x - 4)^2 + (y - 9)^2 = 16$.

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