
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 numbers \(a\) and \(b\) can be expressed as the product of three prime numbers less than 10. Each prime number less than 10 is present in the factorization of at least one of the numbers \(a\) and \(b\). The greatest common divisor of the numbers \(a\) and \(b\) is equal to the greatest common divisor of the numbers \(\frac{a}{15}\) and \(b\), and simultaneously, it is twice the greatest common divisor of the numbers \(a\) and \(\frac{b}{4}\).

Determine the numbers \(a\) and \(b\).

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