
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 the function $f(x)=8\ln x+15x-x^{2}$, and the sequence $\{a_{n}\}$ satisfies $a_{n}=f(n)$, $n\in\mathbb{N}_{+}$. When the sum of the first $n$ terms of the sequence $\{a_{n}\}$, denoted as $S_{n}$, is maximum, calculate the value of $n$.

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