
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 identical-looking coins, knowing that among them are 30 genuine coins and 70 counterfeit coins. The masses of all genuine coins are the same, while the masses of all counterfeit coins are different, with each counterfeit coin being heavier than a genuine coin. The exact masses of the coins are unknown. There is a two-pan balance scale available, which can be used to compare the masses of two groups of coins that have the same number of coins. What is the minimum number of weighings needed for the numismatist to reliably find at least one genuine coin?

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