
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
Given \( n \) coins with pairwise different masses and \( n \) pan scales, where \( n > 2 \). During each weighing, one can choose any set of scales, place one coin on each pan, read the measurement, and then remove the coins. One of these scales (unknown which) is faulty and can randomly provide either correct or incorrect results. What is the minimum number of weighings required to reliably find the heaviest coin?

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