
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
Define a function $g$ on the set of ordered pairs of positive integers such that it fulfills the following conditions:
\begin{align*}
g(x,x) &= x^2,\\ 
g(x,y) &= g(y,x),\\ 
(x + y) g(x,y) &= yg(x,x + y).
\end{align*}
Calculate $g(2,12) + g(5,25)$.

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