
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
There are several distinct natural numbers written on the board. If the smallest number is increased 30 times, the sum of the numbers on the board will be 450. If the largest number is increased 14 times, the sum of the numbers on the board will also be 450. What could be the numbers written on the board?

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