
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 5 units intersect at the origin. What is the number of square units in the area of the non-shaded region? Express your answer in terms of $\pi$. 
[asy]
import olympiad; import geometry; size(100); defaultpen(linewidth(0.8));
fill(Arc((1,0),1,90,180)--Arc((0,1),1,270,360)--cycle,gray(0.6));
fill(Arc((-1,0),1,0,90)--Arc((0,1),1,180,270)--cycle,gray(0.6));
fill(Arc((-1,0),1,270,360)--Arc((0,-1),1,90,180)--cycle,gray(0.6));
fill(Arc((1,0),1,180,270)--Arc((0,-1),1,0,90)--cycle,gray(0.6));
filldraw(Circle((-1,0),1), white);
filldraw(Circle((1,0),1), white);
filldraw(Circle((0,-1),1), white);
filldraw(Circle((0,1),1), white);
draw((-2.3,0)--(2.3,0)^^(0,-2.3)--(0,2.3));
draw(Circle((-1,0),1)); draw(Circle((1,0),1)); draw(Circle((0,-1),1)); draw(Circle((0,1),1));
[/asy]

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