
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
There are 13 coins of the same denomination, among which one is counterfeit and differs in weight from the others. Is it possible to detect the counterfeit coin using three weighings on a balance scale without weights?

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