
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
In a plane, a square with vertices labeled in sequence \( A, B, C, D \) and a point \( O \) are given. It is known that \( OB = OD = 13 \), \( OC = 5\sqrt{2} \), and the area of the square is greater than 225. Find the side length of the square and determine the location of point \( O \) - whether it is inside or outside the square.

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