
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 banker learned that among a set of identical-looking coins, one is counterfeit (lighter in weight). He asked an expert to identify this counterfeit coin using a balance scale without weights, under the condition that each coin can be weighed no more than twice. What is the maximum number of coins the banker can have so that the expert is able to certainly identify the counterfeit coin in $n$ weighings?

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