
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
Around an equilateral triangle $ABC$, draw another equilateral triangle $A'B'C'$ with the same orientation. The intersection points of the corresponding side lines form another equilateral triangle. The second triangle can be inscribed in 3 different ways, generally resulting in three equilateral triangles. How do the side lengths of these three triangles compare to each other?

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