
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 12 units long. Two equilateral triangles each with sides 4 units long are cut off at the top and bottom, leaving a hexagonal shape in the middle. What is the ratio of the area of one of the smaller cut off triangles to the area of the hexagonal shape? Express your answer as a common fraction.

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