
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
A numismatist has 100 coins that look identical. He knows that among them there are 30 genuine coins and 70 counterfeit coins. Furthermore, he knows that all genuine coins have the same weight, all counterfeit coins have different weights, and each counterfeit coin is heavier than a genuine coin; however, the exact weights of the coins are unknown. There is a two-pan balance scale without weights, which can compare the masses of two groups each containing the same number of coins. What is the minimum number of weighings on this balance scale the numismatist needs to guarantee finding at least one genuine coin?

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