
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
Among 100 light bulbs, there are $n$ defective ones (where $2 \leq n \leq 92$). If you randomly pick 10 bulbs at once, let the probability of exactly having 2 defective bulbs be denoted as $f(n)$. Determine the value of $n$ for which $f(n)$ is maximized.

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