
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
In the arithmetic sequence \(\left\{a_{n}\right\}\), \(a_{2}=5\) and \(a_{6}=21\). Let the sum of the first \(n\) terms of the sequence \(\left\{\frac{1}{a_{n}}\right\}\) be denoted as \(S_{n}\). If the inequality \(S_{2 n+1}-S_{n} \leqslant \frac{m}{15}\) holds for any \(n \in \mathbf{N}_{+}\), then the minimum value of the positive integer \(m\) is \(\qquad\).

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