
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
Find all three-digit numbers that are equal to the sum of all their digits plus twice the square of the sum of their digits. List all possible numbers in ascending order without spaces and enter the resulting concatenated multi-digit number.

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