
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
Is it possible to find four different natural numbers, each of which is not divisible by 2, 3, or 4, but the sum of any two is divisible by 2, the sum of any three is divisible by 3, and the sum of all four is divisible by 4?

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