
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 silver coins arranged by weight and 101 gold coins also arranged by weight. It's known that all coins have different weights. We have a balance scale that can compare any two coins and determine which one is heavier. How can we find a coin with the least number of weighings?

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