
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 empty squares in the image that should be filled with natural numbers so that the sum of the three numbers on each side of the triangle is the same. How many different sets of natural number triplets can be added to the image?

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