
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
The region is bounded by arcs of circles each having a radius of 5 units, with each arc having a central angle measure of 120 degrees, and intersecting at points of tangency. The area of this region can be expressed in the form $a\sqrt{b}+c\pi$ square units, where $\sqrt{b}$ is in its simplest form. Determine the value of $a + b + c$.
[asy]
size(200);
draw(arc((-3.75,0),5,0,120));
draw(arc((0,6.495),5,-120,-240));
draw(arc((3.75,0),5,120,240));
[/asy]

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