
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
Hinkley Publishers has devised a pricing scale for its new release "Finding Fiona" as follows:
$C(n) = \left\{\begin{matrix}
15n, & \text{if } 1 \le n \le 30 \\
13n, & \text{if } 31 \le n \le 60 \\
12n, & \text{if } 61 \le n 
\end{matrix}\right.$
where $n$ is the number of books ordered, and $C(n)$ is the price in dollars for $n$ books. Calculate for how many values of $n$ it is cheaper to buy more than $n$ books compared to buying exactly $n$ books.
A) 4  
B) 5  
C) 6  
D) 7  
E) 8

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