
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
Vasya had 101 real coins. One of them was replaced with a fake one (it differs in weight, but it's unknown whether it is lighter or heavier than a real one). Vasya wants to find as many real coins as possible in one weighing using a balance scale without weights. What should he do and how many real coins can he find?

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