
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 the six circles of a diagram, the numbers 4, 14, and 6 are written. In how many ways can natural numbers be placed in the remaining three circles so that the product of the three numbers along each of the three sides of the triangular diagram is the same?

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