
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 several bags, each containing quite a few coins. In one bag, the coins are counterfeit, while in all other bags the coins are genuine. The weight of a genuine coin is known, and it is known that a counterfeit coin is 1 gram lighter than a genuine coin. How can you identify the bag with counterfeit coins using a single weighing on a scale with weights?

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