
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
The two-variable function \(f(x, y)\), defined on the natural numbers, satisfies the following conditions:

\[ f(x, x) = x \]

\[ f(x, y) = f(y, x) \]

\[ (x + y) \cdot f(x, y) = f(x, x + y) \cdot y \]

What is \( f(980, 1980) \)?

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