
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
Among 12 coins, there is one counterfeit coin. It is known that the counterfeit coin has a different weight compared to the genuine ones, but it is not known whether it is lighter or heavier. All genuine coins have the same weight. Identify the counterfeit coin and determine if it is lighter or heavier using three weighings on a two-pan balance without weights.

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