
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
We know the following about three natural numbers:

a) all three are different;

b) their sum is 406;

c) their greatest common divisor is a prime number greater than 2 (let's denote it by \( p \));

d) if each number is divided by \( p \), we get three prime numbers again (let these be \( p_{1}, p_{2}, p_{3} \)). What are these numbers?

Note that 1 is not considered a prime number.

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