
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
If we also want to know whether the counterfeit coin is lighter or heavier than the others in the previous problem, what is the maximum number of coins that can be determined with three weighings?

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