
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 \( f \) be a function defined on the set of ordered pairs of positive integers that satisfies:
\[
f(x, x) = x, \quad f(x, y) = f(y, x), \quad \text{and} \quad (x + y) f(x, y) = x f(x, x + y).
\]
Calculate \( f(18, 48) \).

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