
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 function $g$, defined on the set of ordered pairs of positive integers, satisfies the following properties:
\begin{align*}
    g(x,x) &= x, \\
    g(x,y) &= g(y,x), \quad \text{and} \\
    (x + y) g(x,y) &= y g(x, x + y).
\end{align*}
Calculate $g(18, 60)$.

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