
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
Professor Loxley decides to pick five different integers from the numbers 1 through 30. He selects his numbers so that the product of these numbers is a power of 6. What is the probability that the combination of numbers he chooses is the same as the one on a winning ticket, assuming the winning ticket also has combinations where the product is a power of 6?
A) 1/10  
B) 1/5  
C) 1/4  
D) 1/3  
E) 1/2

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