
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
If \( p \) and \( q \) are coprime, and \( p \) and \( q \) are natural numbers (\(\mathbf{N}\)), then there exists a smallest \( m = pq - p - q + 1 \) such that for all \( n \geq m \), \( n \) can be written as \( n = px + qy \) (where \( x \) and \( y \) are non-negative integers).

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