
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
If real numbers \( a_{ij} > 0 \) (for \( i=1, 2, \ldots, n \) and \( j=1, 2, \ldots, m \)), and a real number \( p > 1 \), then

$$
\begin{array}{l}
\left(\sum_{i=1}^{n}\left(a_{i1} + a_{i2} + \cdots + a_{im}\right)^{p}\right)^{\frac{1}{p}} \\
\leqslant \left(\sum_{i=1}^{n} a_{i1}^{p}\right)^{\frac{1}{p}} + \left(\sum_{i=1}^{n} a_{i2}^{p}\right)^{\frac{1}{p}} + \cdots + \left(\sum_{i=1}^{n} a_{im}^{p}\right)^{\frac{1}{p}}.
\end{array}
$$

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