
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 100 visually indistinguishable coins of three types: gold, silver, and copper (each type is represented at least once). It is known that gold coins weigh 3 grams each, silver coins weigh 2 grams each, and copper coins weigh 1 gram each.

How can the type of all coins be determined using no more than 101 weighings on a balance scale without weights?

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