
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 the smallest positive integer that can be expressed as the sum of 2002 positive integers, each having the same digit sum, and can also be expressed as the sum of 2003 positive integers, each having the same digit sum. This is a problem from the 28th Russian Mathematical Olympiad.

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