
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
Each of the three boys either always tells the truth or always lies. They were told six natural numbers. After that, each boy made two statements.

Petya: 1) These are six consecutive natural numbers. 2) The sum of these numbers is even.

Vasya: 1) These numbers are $1, 2, 3, 5, 7, 8$. 2) Kolya is a liar.

Kolya: 1) All six numbers are distinct and each is not greater than 7. 2) The sum of these six numbers is 25.

What are the numbers that were given to the boys?

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