
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 any carry-over, then $n$ is called a "powerful number". For example, $32$ is a "powerful number" because $32 + 33 + 34$ does not produce any carry-over; $23$ is not a "powerful number" because $23 + 24 + 25$ produces a carry-over. Suppose all "powerful numbers" less than $1000$ have their digits forming set $A$, then the sum of the digits in set $A$ is $\boxed{6}$.

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