
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
You have a balance scale without weights and 11 coins that look identical. Among them, one coin may be counterfeit, and it is unknown whether the counterfeit coin is heavier or lighter than the genuine coins (genuine coins all have the same weight). How can you determine at least 8 genuine coins with just two weighings?

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