
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 diagram shows a region bounded by the arcs of circles having a radius of 5 units, with a central angle measure of 45 degrees. These arcs intersect at points of tangency inside a regular octagon. Calculate the area of this region, which can be expressed in the form \( a\sqrt{b} + c\pi \) square units, where \( \sqrt{b} \) is a radical in its simplest form. What is the value of \( a + b + c \)?

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