
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 square is given in the plane with consecutively placed vertices \( A, B, C, D \) and a point \( O \). It is known that \( OA = OC = 10 \), \( OD = 6\sqrt{2} \), and the side length of the square does not exceed 3. Find the area of the square. Is point \( O \) located outside or inside the square?

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