
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
TT Publishers sets prices for their new release, "Journey's Echo", by the following structure:
\[ C(n) = \left\{\begin{matrix}
15n, & \text{if } 1 \le n \le 30\\
14n, & \text{if } 31 \le n \le 60\\ 
12n, & \text{if } 61 \le n \le 120 \\
11n, & \text{if } 121 \le n
\end{matrix}\right. \]
where \( n \) is the quantity of books ordered, and \( C(n) \) is the cost in dollars of \( n \) books. Considering that buying more books can sometimes be cheaper, determine for how many values of \( n \), is it cheaper to buy more than \( n \) books than to buy exactly \( n \) books.
A) 5
B) 6
C) 7
D) 8
E) 9

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