
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
A function $g$ defined for ordered pairs of positive integers satisfies:
\begin{align*}
g(x, x) &= x, \\
g(x, y) &= g(y, x), \\
(x+y) g(x, y) &= x g(y, x+y).
\end{align*}
Calculate $g(18, 75)$.

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