
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 \( n \) be a positive integer. Determine the size of the largest subset of \(\{ -n, -n+1, \ldots, n-1, n \}\) which does not contain three elements \( a, b, c \) (not necessarily distinct) satisfying \( a + b + c = 0 \).

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