
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 between $1$ and $2020$, inclusive. Calculate the probability $p$ that the product of these three integers is divisible by $5$.
A) $\frac{1}{3}$
B) $\frac{1}{2}$
C) $\frac{2}{3}$
D) $\frac{7}{5}$
E) $\approx 0.488$

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