
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
Suppose Wei decides to alter his logo design by increasing the side length of the square to 40 inches and adding one more circle of the same size as the others but positioned in the center. Each circle remains tangent to its nearest sides or circles. Calculate the shaded area in square inches.

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