
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
Let \( n > m \geq 1 \) be natural numbers such that the groups of the last three digits in the decimal representation of \( 1978^m \) and \( 1978^n \) coincide. Find the ordered pair \( (m, n) \) of such \( m \) and \( n \) for which \( m+n \) is minimal.

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