
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
Let
\[g(a,b) = \left\{
\renewcommand{\arraystretch}{3}
\begin{array}{cl}
\dfrac{a^2b - a + 3}{3a} & \text{if $a + b \le 5$}, \\
\dfrac{ab^2 - b - 3}{-3b} & \text{if $a + b > 5$}.
\end{array}
\renewcommand{\arraystretch}{1}
\right.\]
Find $g(3,2) + g(3,3).$

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