
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
An antique dealer acquired 99 identical ancient coins. He was informed that exactly one of the coins is fake and lighter than the genuine ones (the genuine coins all have the same weight). How, using a balance scale without weights, can he identify the fake coin with 7 weighings if he is not allowed to weigh any coin more than twice?

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