
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
Beacon Books has a new pricing strategy for its latest mystery novel "Find Fiona?": 
$C(n) =\left\{\begin{matrix}15n, &\text{if }1\le n\le 50\\ 14n, &\text{if }51\le n\le 100\\ 12n, &\text{if }101\le n\le 150\\ 10n, &\text{if }151\le n\end{matrix}\right.$
where $n$ is the number of books ordered, and $C(n)$ is the cost in dollars for $n$ books. Determine for how many values of $n$ is it cheaper to buy more than $n$ books than to buy exactly $n$ books?
- **A)** 8
- **B)** 10
- **C)** 12
- **D)** 14
- **E)** 16

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