
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
Mientka Publishing has updated the pricing strategy on their hit series "Finding Frida" with the following model:
\[ C(n) = \begin{cases} 
15n & \text{if } 1 \leq n \leq 20 \\
13n - 10 & \text{if } 21 \leq n \leq 40 \\
12n - 30 & \text{if } n > 40 
\end{cases} \]
where \(n\) represents the number of books ordered and \(C(n)\) the total cost in dollars. For how many book quantities \(n\) does purchasing exactly \( n + 1\) books result in a lower cost than purchasing exactly \(n\) books?
A) 2
B) 3
C) 4
D) 5
E) 6

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