
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
Find the number of pairs of integers $(a; b)$ such that $1 \leq a \leq 80$, $1 \leq b \leq 30$, and the area $S$ of the region defined by the system of inequalities

$$
\left\{\begin{array}{l}
\frac{x}{a}+\frac{y}{b} \geq 1 \\
x \leq a \\
y \leq b
\end{array}\right.
$$

is such that the number $2S$ is divisible by 5.

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