
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
If in the set \( A \), there exist \( m \) elements \( a_{1}, a_{2}, \cdots, a_{m} \) (which may be repeated), satisfying the equation \( a_{1} + a_{2} + \cdots + a_{m-1} = a_{m} \), then the set \( A \) is called \( m \)-sum-related. Given that the set \( \left\{1, 2, \cdots, n_{m}\right\} \) is partitioned arbitrarily into two disjoint subsets, and at least one of these subsets is \( m \)-sum-related \((m \geqslant 3)\), find the minimum value of the natural number \( n_{m} \).

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