
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 \(f(a,b)\) as follows:
\[
f(a,b) = \left\{
\renewcommand{\arraystretch}{3}
\begin{array}{cl}
\dfrac{ab - a - 1}{3a} & \text{if $a - b \le 2$}, \\
\dfrac{ab + b - 1}{-3b} & \text{if $a - b > 2$}.
\end{array}
\renewcommand{\arraystretch}{1}
\right.\]
Calculate \(f(3,2) + f(5,1).\)

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