
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
Three distinct integers are selected at random from 1 to 1000, inclusive. Which of the following correctly describes the probability \( p \) that the product of these three integers is odd?
A) \( p < \frac{1}{8} \)  
B) \( p = \frac{1}{8} \)  
C) \( \frac{1}{8} < p < \frac{1}{5} \)  
D) \( p = \frac{1}{5} \)  
E) \( p > \frac{1}{5} \)

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