
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
My favorite numbers are those that, when multiplied by the sum of their own digits, grow tenfold. The product of three of my favorite numbers is 71668. What are these numbers?

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