
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, three circles each with a radius of 5 units intersect at exactly one common point, which is the origin. Calculate the total area in square units of the shaded region formed within the triangular intersection of the three circles. Express your answer in terms of $\pi$.
[asy]
import olympiad; import geometry; size(100); defaultpen(linewidth(0.8));
filldraw(Circle((0,0),5));
filldraw(Circle((4,-1),5));
filldraw(Circle((-4,-1),5));
[/asy]

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