
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 with a side length of 2 is divided into smaller triangles with a side length of 1. Six identical-looking coins are placed at the vertices of these smaller triangles. It is known that two of these coins are counterfeit, lighter than the genuine ones, and are placed at the ends of a unit segment. How can you find both counterfeit coins using 2 weighings on a balance scale without additional weights? (The counterfeit coins weigh the same, and the genuine coins also weigh the same).

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