
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 $a_{1}, a_{2}, \cdots, a_{n}$ be non-negative real numbers. If $0 < r < s$, then
$$
\left(\sum_{i=1}^{n} a_{i}^{s}\right)^{\frac{1}{s}} \leq \left(\sum_{i=1}^{n} a_{i}^{r}\right)^{\frac{1}{r}},
$$
with equality holding if and only if at least $n-1$ of $a_{1}, a_{2}, \cdots, a_{n}$ are 0.

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