
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
In the story of Tsar Saltan, among the bags of gold coins cast in nutshells in Prince Gvidon's cellar, there is one bag in which all the coins are counterfeit. Both the bag and the coins look exactly like the real ones, but a real coin weighs 20 zolotniks, while a counterfeit coin weighs 15 zolotniks. How can you determine which bag contains the counterfeit coins with just one weighing?

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