
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 large square playground has a side of length \(12\) meters. Every side is trisected, creating intersection points on the perimeter. Morgan designs a triangular garden by connecting the trisection points that are \(4\) meters apart from each nearest vertex of the square, forming a smaller, inner triangle. Calculate the area of this triangular garden relative to the total area of the square playground.
A) \(\frac{\sqrt{2}}{9}\)
B) \(\frac{\sqrt{3}}{9}\)
C) \(\frac{2\sqrt{2}}{9}\)
D) \(\frac{1}{12}\)

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