
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
Find the smallest natural number $n$ such that any arbitrary partition of the set $\{1, 2, \cdots, n\}$ into two disjoint subsets results in one of the subsets containing three distinct numbers where the product of two of these numbers equals the third. 
(This is from the 29th International Mathematical Olympiad, 1988)

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