
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
Zeus has a scale that allows him to know the weight of the cargo placed on it and a bag with 100 coins, among which there are 10-gram and 9-gram coins. Zeus knows the total number \( N \) of 10-gram coins in the bag but does not know their specific weights. He would like to make four weighings on the scale and as a result, be guaranteed to find at least one 9-gram coin. For what largest \( N \) is this possible? (K. Knop)

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