
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 coins of $1, 2, 3,$ and 5 cruzeiros, one of each denomination, which, if they are genuine, weigh 1, 2, 3, and 5 grams respectively. It turned out that one of them is counterfeit, differing in weight from the normal one (but it is not known whether it is heavier or lighter). How can the counterfeit coin be identified with the minimum number of weighings using a balance scale without weights?

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