
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 $n$ makes the addition operation $n + (n+1) + (n+2)$ without carrying over, then $n$ is called a "powerful number". For example, $32$ is a "powerful number" because $32+33+34$ does not result in a carry-over; $23$ is not a "powerful number" because $23+24+25$ results in a carry-over. Suppose all "powerful numbers" less than $1000$ form set $A$, where the digits of each number in set $A$ are considered individually. In that case, the sum of the digits in set $A$ is $\boxed{\text{answer}}$.

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