
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 natural number. Find the smallest constant \( C \) such that for all \( x_{1}, \ldots, x_{n} \geqslant 0 \),

\[
\sum_{1 \leqslant i<j \leqslant n} x_{i} x_{j}\left(x_{i}^{2}+x_{j}^{2}\right) \leqslant C\left(\sum_{i=1}^{n} x_{i}\right)^{4}.
\]

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