
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 an integer. Determine the largest possible constant \( C \) such that for all \( a_1, a_2, \ldots, a_n \geq 0 \) we have \(\left(\sum a_i\right)^{2} \geqslant C \sum_{i<j} a_i a_j\).

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