
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 the set \( S = \{1, 2, \cdots, 3n\} \), where \( n \) is a positive integer. Let \( T \) be a subset of \( S \) such that for any \( x, y, z \in T \) (where \( x, y, z \) can be the same), the condition \( x + y + z \notin T \) is satisfied. Find the maximum number of elements in such a subset \( T \).

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