
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
Peter has 8 coins, of which he knows that 7 are genuine and weigh the same, while one is fake and differs in weight, though he does not know whether it is heavier or lighter. Peter has access to a balance scale, which shows which side is heavier but not by how much. For each weighing, Peter must pay Vasya one of his coins before the weighing. If Peter pays with a genuine coin, Vasya will provide an accurate result; if a fake coin is used, Vasya will provide a random result. Peter wants to determine 5 genuine coins and ensure that none of these genuine coins are given to Vasya. Can Peter guaranteedly achieve this?

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