
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
Given natural numbers \( m \) and \( n \) where \( n > m > 1 \), the last three digits of the decimal representation of \( 1978^m \) and \( 1978^n \) are the same. Find \( m \) and \( n \) such that \( m+n \) is minimized.

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