
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
Given \( n \in \{3900, 3901, \cdots, 3909\} \), find the values of \( n \) for which the set \( \{1, 2, \cdots, n\} \) can be partitioned into several triples, each containing one number that equals the sum of the other two numbers.

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