
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 two circles and a square with sides of length $10 \text{ cm}$. One vertex of the square is at the center of the large circle, and two sides of the square are tangents to both circles. The small circle touches the large circle. The radius of the small circle is \((a - b\sqrt{2}) \text{ cm}\).

What is the value of \(a + b\)?

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