
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
Given the cost function C(n) for ordering n books as C(n) = { 15n if 1 ≤ n ≤ 30, 14n if 20 ≤ n ≤ 60, 13n if n ≥ 50 }, determine how many values of n result in a lower cost by ordering more than n books than exactly n books.

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