
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 $n$ coins ($n > 2$) of different masses and $n$ scales. Each time you weigh, you choose one scale and place one coin on each side to compare their weights, then remove the coins. It is known that one of the scales is faulty (but it is unknown which one), sometimes showing the correct result and sometimes giving a wrong result. What is the minimum number of weighings needed to definitely find the heaviest coin?

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