
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 circle is drawn through two adjacent vertices of a square such that the length of the tangent to it from the third vertex of the square is three times the side length of the square. Find the area of the circle if the side length of the square is \(a\).

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