
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 \( n \ge 2 \) be an integer and let \( T = \{2, 3, 4, \ldots, n\} \). Find the smallest value of \( n \) such that for every partition of \( T \) into two subsets, at least one of the subsets contains integers \( a \), \( b \), and \( c \) (not necessarily distinct) such that \( a + b = c \).

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