
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
Given a $3 \times 3$ square is placed inside a larger diagram, with circles centered at each corner with radius equal to the distance from the corner to the center of the square, construct a new square $EFGH$ such that each of its sides is exactly tangent to one of these circles, with sides parallel to the original square. Determine the area of square $EFGH$.

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