
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
A bag contains $n$ ($n>1$) red balls and 5 white balls. Each time a lottery draw is performed, two balls are drawn simultaneously and then replaced back into the bag. If the two balls are of different colors, it's considered a win. The probability that exactly one out of three lottery draws results in a win is denoted as $p$. Determine the value of $n$ for which $p$ reaches its maximum value.

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