
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
In three out of six circles on the diagram, the numbers 4, 14, and 6 are written. In how many ways can the remaining three circles be filled with natural numbers such that the product of the three numbers along each side of the triangular diagram is the same?

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