
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
Casper can purchase exactly $10$ pieces of orange candy, $16$ pieces of yellow candy, $18$ pieces of violet candy, or $n$ pieces of purple candy. Each piece of purple candy costs $24$ cents. The cost of one piece of orange, yellow, and violet candy are $o$, $y$, and $v$ respectively, with the relationships: $10o = 16y = 18v = 24n$. What is the smallest possible value of $n$?
A) 25
B) 30
C) 35
D) 40
E) 45

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