
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 any real numbers \( x \) and \( y \), the function \( f(x) \) satisfies \( f(x) + f(y) = f(x + y) + xy \).
If \( f(1) = m \), how many positive integer pairs \( (m, n) \) satisfy \( f(n) = 2019 \)?

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