
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
You have a balance scale without weights and 3 identical-looking coins, one of which is a counterfeit and lighter than the real ones (the real coins are of the same weight). How many weighings are needed to determine the counterfeit coin?

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