
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
Given two natural numbers \( n \) and \( m \) greater than 1, find all natural numbers \( l \) such that for any positive numbers \( a_{1}, a_{2}, \ldots, a_{n} \), the following inequality holds:
$$
\sum_{k=1}^{n} \frac{1}{s_{k}}\left(l k+\frac{1}{4} l^{2}\right)<m^{2} \sum_{k=1}^{n} \frac{1}{a_{k}},
$$
where \( s_{k}=a_{1}+a_{2}+\cdots+a_{k} \).

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