
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
An equilateral triangle has sides of 10 units long. A smaller equilateral triangle with sides of 3 units is cut off from each vertex, leaving a smaller equilateral triangle in the center. What is the ratio of the area of one of the corner triangles to the area of the central triangle?

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