
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 10 bags of coins. In nine bags, the coins are real (weigh 10g each), and in one bag, all the coins are counterfeit (weigh 112g each). Determine which bag contains the counterfeit coins with one weighing.

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