
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 informed of six natural numbers. Afterward, each boy made two statements.

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

Vasya: 1) These numbers are 1, 2, 3, 4, 5, 6.
2) Kolya is a liar.

Kolya: 1) All these numbers are distinct and divisible by 3.
2) Each of these numbers is less than 20.

What numbers were the boys informed of?

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