
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
A 3-digit number $\bar{abc}$ is formed using the digits $1,2,...,9$ without repetition. The product of the digits $a, b,$ and $c$ is divisible by $10$. Determine the number of such 3-digit numbers that exist.

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