
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
Determine the smallest natural number which can be represented both as the sum of  $2002$  positive integers with the same sum of decimal digits, and as the sum of  $2003$  integers with the same sum of decimal digits.

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