
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 publishing company has set the pricing for a popular book as follows:
$$
C(n)=\left\{\begin{array}{l}
12n, \text{ if } 1 \leq n \leq 24; \\
11n, \text{ if } 25 \leq n \leq 48; \\
10n, \text{ if } n \geq 49.
\end{array}\right.
$$

Here, \(n\) represents the number of books ordered, and \(C(n)\) is the total cost in yuan.

1. For how many values of \(n\) is it cheaper to buy more than \(n\) books compared to buying exactly \(n\) books?
2. If the cost of producing one book is 5 yuan, and two individuals each buy at least one book, with a total purchase of 60 books between them, what is the minimum and maximum profit the publishing company can make?

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