
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
Square  $1$  is drawn with side length  $4$ . Square  $2$  is then drawn inside of Square  $1$ , with its vertices at the midpoints of the sides of Square  $1$ . Given Square  $n$  for a positive integer  $n$ , we draw Square  $n+1$  with vertices at the midpoints of the sides of Square  $n$ . For any positive integer  $n$ , we draw Circle  $n$  through the four vertices of Square  $n$ . What is the area of Circle  $7$ ?

*2019 CCA Math Bonanza Individual Round #2*

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