
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 with the following properties:
\[
g(x,x) = x^2,
\]
\[
g(x,y) = g(y,x),
\]
\[
(x + y) g(x,y) = yg(x, x + y).
\]
Calculate $g(10,44)$.

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