
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
In the diagram, four circles of radius 6 units each intersect at the origin. In each quarter-section of the diagram, the circle's quarter-section is overlaid with a semicircle of radius 3 units, centered at the midpoint of the hypotenuse of the isosceles right triangle formed inside this quarter-section. What is the number of square units in the area of the shaded region? Express your answer in terms of $\pi$.

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