
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
Let \( M = \{1, 2, 3, \ldots, 40\} \). Find the smallest positive integer \( n \) such that \( M \) can be partitioned into \( n \) pairwise disjoint subsets, and for any 3 numbers \( a, b, c \) (not necessarily distinct) within the same subset, \( a \neq b + c \).

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