
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
Two congruent equilateral triangles are constructed on a plane, with one triangle's vertex at the center of the other. Find the ratio of the maximum area to the minimum area of their overlapping parts.

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