
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 the function $g(x,y)$ as follows:
\[ g(x,y) = \left\{
\begin{array}{cl}
\dfrac{2xy - x + 3}{3x} & \text{if $x + y \leq 4$}, \\
\dfrac{xy - y - 3}{-3y} & \text{if $x + y > 4$}.
\end{array}
\right. \]
Calculate $g(3,1) + g(3,3)$.

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