
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
If a natural number $n$ is such that the operation $n + (n+1) + (n+2)$ does not generate any carries, then $n$ is called a "smooth number." For example, 32 is a "smooth number" because the addition of 32, 33, and 34 doesn't generate any carries; however, 23 is not a "smooth number" because the addition of 23, 24, and 25 does involve carries. Let's define set $A$ as the set containing the digits of all "smooth numbers" less than 1000. Determine the number of distinct three-digit even numbers that can be formed using the digits in set $A$.

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