
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 class contains $n > 15$ students, with an overall average score of $10$. Among them, the mean score of $15$ randomly selected students is $12$. Determine the mean of the rest of the scores, denoted as $p$, in terms of $n$.
A) $\frac{180-10n}{n-15}$  
B) $\frac{10n-150}{n-15}$  
C) $\frac{10n-180}{n-15}$  
D) $\frac{10(n-15)}{n^2}$  
E) $\frac{12(n-15)}{10n}$

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