
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
A new logo designed by Mina consists of a large square and four identical circles. Each circle is tangent to two adjacent sides of the square and to two neighboring circles. If the side length of the square in the logo is 30 inches, calculate the total shaded area in square inches.

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