
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
Let's consider a larger equilateral triangle with each side 12 units long. An equilateral triangle with sides 3 units long is cut off from one corner, leaving an irregular polygon. What is the ratio of the area of the smaller triangle to the area of the remaining polygon?

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