
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
Grammatica Publishing offers the following price for their popular title, Grammar in Minutes:
\[ C(n) = \begin{cases} 
15n & \text{if } 1 \leq n \leq 20 \\
13n & \text{if } 21 \leq n \leq 40 \\
11n & \text{if } 41 \leq n 
\end{cases} \]
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 $n$ it is cheaper to buy more than $n$ books than to buy exactly $n$ books.
A) 3
B) 4
C) 5
D) 6
E) 7

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