
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
On the board, there are three natural numbers $a, b, c$, for which the following holds:
- the greatest common divisor of the numbers $a$ and $b$ is 15,
- the greatest common divisor of the numbers $b$ and $c$ is 6,
- the product of the numbers $b$ and $c$ is 1800,
- the least common multiple of the numbers $a$ and $b$ is 3150.

What are these numbers?

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