
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
Eight circles, each with a radius of 1, are drawn inside a rectangle. Four of the circles are tangent to two sides of the rectangle and to two other circles, while the other four circles are tangent to one side of the rectangle and to three other circles. Calculate the area of the shaded region consisting of three spaces (each space bounded by a different set of four circles) and four of the circles themselves.

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