
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. Each selected integer must be odd, and the sum of its digits must also be odd. Calculate the probability that the product of these three integers is odd.

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