
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 intersect at the origin. Calculate the area of the shaded region in square units, expressed in terms of $\pi$. Assume each shaded region is bounded by arcs of these circles and intersects at the midpoint of the circle’s radius.

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